{"id":2,"date":"2017-08-03T16:14:39","date_gmt":"2017-08-03T16:14:39","guid":{"rendered":"http:\/\/sites.nd.edu\/bei-hu\/?page_id=2"},"modified":"2026-02-12T14:41:42","modified_gmt":"2026-02-12T18:41:42","slug":"publication","status":"publish","type":"page","link":"https:\/\/sites.nd.edu\/bei-hu\/professor-bei-hu\/publication\/","title":{"rendered":"Publications"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Updated February 12, 2026&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Book edited<\/strong><br>[1] Mark Alber, Bei Hu, and Joachim Rosenthal (eds.),&nbsp;<em>Current and future directions in applied mathematics<\/em>, Birkh\u00e4user Boston Inc., Boston, MA, 1997.&nbsp;<a href=\"http:\/\/doi.org\/10.1007\/978-1-4612-2012-1\">http:\/\/doi.org\/10.1007\/978-1-4612-2012-1<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Book translated<\/strong><br>[1]&nbsp;Ya-Zhe&nbsp;Chen and&nbsp;Lan-Cheng&nbsp;Wu,&nbsp;<em>Second order elliptic equations and elliptic systems<\/em>, translated by Bei Hu, Translations of Mathematical Monographs, vol.&nbsp;174, American Mathematical Society, Providence, RI, 1998.&nbsp;<a href=\"https:\/\/www.ams.org\/books\/mmono\/174\/\">https:\/\/www.ams.org\/books\/mmono\/174\/<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Books<\/strong><br>[1]&nbsp;Bei&nbsp;Hu,&nbsp;<em>Blow-up Theories for Semilinear Parabolic Equations,&nbsp;<\/em>Lecture Notes in Mathematics volume 2018, Springer, 2011, &nbsp;<a href=\"http:\/\/doi.org\/10.1007\/978-3-642-18460-4\">http:\/\/doi.org\/10.1007\/978-3-642-18460-4<\/a>.<br>[2]&nbsp;Jin&nbsp;Liang and&nbsp;Bei&nbsp;Hu,&nbsp;<em>Credit Rating Migration Risks in Structure Models<\/em>, Springer, 2024, &nbsp;<a href=\"http:\/\/doi.org\/10.1007\/978-981-97-2179-5\">http:\/\/doi.org\/10.1007\/978-981-97-2179-5<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Referred papers<\/strong><br>[1]\u00a0Bei\u00a0Hu,\u00a0<em>Fully nonlinear elliptic equations with gradient constraint<\/em>, Beijing Daxue Xuebao (Journal of Peking University)\u00a0<strong>5\u00a0<\/strong>(1986), 78\u201391 (English).\u00a0<a href=\"https:\/\/en.cnki.com.cn\/Article_en\/CJFDTotal-BJDZ198605006.htm\">https:\/\/en.cnki.com.cn\/Article_en\/CJFDTotal-BJDZ198605006.htm<\/a>.<br>[2]\u00a0Bei\u00a0Hu,\u00a0<em>Boundary value problems for fully nonlinear elliptic equations with sufficiently large coefficients in the zero-order terms<\/em>, Journal of Mathematical Research and Exposition\u00a0<strong>7\u00a0<\/strong>(1987), no.\u00a04, 615\u2013626 (Chinese).\u00a0<a href=\"https:\/\/www.cnki.com.cn\/Article\/CJFDTOTAL-SXYJ198704022.htm\">https:\/\/www.cnki.com.cn\/Article\/CJFDTOTAL-SXYJ198704022.htm<\/a>.<br>[3]\u00a0Bei\u00a0Hu,\u00a0<em>Periodic solutions of the parabolic Bellman equation and their stability<\/em>, Advances in Mathematics (Beijing)\u00a0<strong>17\u00a0<\/strong>(1988), no.\u00a02, 164\u2013168 (Chinese, with English summary).\u00a0<a href=\"https:\/\/www.cnki.com.cn\/Article\/CJFDTOTAL-SXJZ198802003.htm\">https:\/\/www.cnki.com.cn\/Article\/CJFDTOTAL-SXJZ198802003.htm<\/a>.<br>[4]\u00a0Bei\u00a0Hu,\u00a0<em>Obstacle problems for a class of nonlinear elliptic equations<\/em>, Journal of Partial Differential Equations Ser. B\u00a0<strong>1\u00a0<\/strong>(1988), no.\u00a01, 1\u201311 (Chinese).<br>[5]\u00a0Avner\u00a0Friedman and\u00a0Bei\u00a0Hu,\u00a0<em>The Stefan problem for a hyperbolic heat equation<\/em>, Journal of Mathematical Analysis and Application\u00a0<strong>138\u00a0<\/strong>(1989), no.\u00a01, 249\u2013279, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/0022-247X(89)90334-X\">http:\/\/doi.org\/10.1016\/0022-247X(89)90334-X<\/a>.<br>[6]\u00a0Bei\u00a0Hu,\u00a0<em>A quasi-variational inequality arising in elastohydrodynamics<\/em>, SIAM Journal on Mathematical Analysis\u00a0<strong>21\u00a0<\/strong>(1990), no.\u00a01, 18\u201336, \u00a0<a href=\"http:\/\/doi.org\/10.1137\/0521002\">http:\/\/doi.org\/10.1137\/0521002<\/a>.<br>[7]\u00a0Bei\u00a0Hu,\u00a0<em>A free boundary problem for a Hamilton-Jacobi equation arising in ion etching<\/em>, Journal of Differential Equations\u00a0<strong>86\u00a0<\/strong>(1990), no.\u00a01, 158\u2013182, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/0022-0396(90)90046-R\">http:\/\/doi.org\/10.1016\/0022-0396(90)90046-R<\/a>.<br>[8]\u00a0Bei\u00a0Hu,\u00a0<em>A fiber-tapering problem<\/em>, Nonlinear Analysis: Theory, Method and Application\u00a0<strong>15<\/strong>\u00a0(1990), no.\u00a06, 513\u2013525, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/0362-546X(90)90056-M\">http:\/\/doi.org\/10.1016\/0362-546X(90)90056-M<\/a>.<br>[9]\u00a0Avner\u00a0Friedman and\u00a0Bei\u00a0Hu,\u00a0<em>A free boundary problem arising in electrophotography<\/em>, Nonlinear Analysis: Theory, Method and Application\u00a0<strong>16\u00a0<\/strong>(1991), no.\u00a09, 729\u2013759, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/0362-546X(91)90080-K\">http:\/\/doi.org\/10.1016\/0362-546X(91)90080-K<\/a>.<br>[10]\u00a0Bei\u00a0Hu,\u00a0<em>Diffusion of penetrant in a polymer: a free boundary problem<\/em>, SIAM Journal on Mathematical Analysis\u00a0<strong>22\u00a0<\/strong>(1991), no.\u00a04, 934\u2013956, \u00a0<a href=\"http:\/\/doi.org\/10.1137\/0522060\">http:\/\/doi.org\/10.1137\/0522060<\/a>.<br>[11]\u00a0Avner\u00a0Friedman and\u00a0Bei\u00a0Hu,\u00a0<em>Homogenization approach to light scattering from polymer-dispersed liquid crystal films<\/em>, SIAM Journal on Applied Mathematics\u00a0<strong>52\u00a0<\/strong>(1992), no.\u00a01, 46\u201364, \u00a0<a href=\"http:\/\/doi.org\/10.1137\/0152004\">http:\/\/doi.org\/10.1137\/0152004<\/a>.<br>[12]\u00a0Bei\u00a0Hu,\u00a0<em>A nonlinear nonlocal parabolic equation for channel flow<\/em>, Nonlinear Analysis: Theory, Method and Application\u00a0<strong>18<\/strong>\u00a0(1992), no.\u00a010, 973\u2013992, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/0362-546X(92)90133-Y\">http:\/\/doi.org\/10.1016\/0362-546X(92)90133-Y<\/a>.<br>[13]\u00a0Avner\u00a0Friedman, Bei\u00a0Hu,\u00a0and\u00a0J. J. L. Vel\u00e1zquez,\u00a0<em>A free-boundary problem modeling loop dislocations in crystals<\/em>, Archive for Rational Mechanics and Analysis\u00a0<strong>119\u00a0<\/strong>(1992), no.\u00a03, 229\u2013291, \u00a0<a href=\"http:\/\/doi.org\/10.1007\/BF00381671\">http:\/\/doi.org\/10.1007\/BF00381671<\/a>.<br>[14]\u00a0Avner\u00a0Friedman and\u00a0Bei\u00a0Hu,\u00a0<em>The Stefan problem with kinetic condition at the free boundary<\/em>, Annali della Scuola Normale Superiore &#8211; Pisa Cl. Sci. (4)\u00a0<strong>19\u00a0<\/strong>(1992), no.\u00a01, 87\u2013111.\u00a0<a href=\"http:\/\/www.numdam.org\/item\/ASNSP_1992_4_19_1_87_0\/\">http:\/\/www.numdam.org\/item\/ASNSP_1992_4_19_1_87_0\/<\/a>.<br>[15]\u00a0Bei\u00a0Hu and\u00a0Lihe\u00a0Wang,\u00a0<em>A free boundary problem arising in electrophotography: solutions with connected toner region<\/em>, SIAM Journal on Mathematical Analysis\u00a0<strong>23\u00a0<\/strong>(1992), no.\u00a06, 1439\u20131454, \u00a0<a href=\"http:\/\/doi.org\/10.1137\/0523082\">http:\/\/doi.org\/10.1137\/0523082<\/a>.<br>[16]\u00a0Avner\u00a0Friedman and\u00a0Bei\u00a0Hu,\u00a0<em>A free boundary problem arising in superconductor modeling<\/em>, Asymptotic Analysis\u00a0<strong>6\u00a0<\/strong>(1992), no.\u00a02, 109\u2013133, \u00a0<a href=\"http:\/\/doi.org\/10.3233\/ASY-1992-6201\">http:\/\/doi.org\/10.3233\/ASY-1992-6201<\/a>.<br>[17]\u00a0Bei\u00a0Hu and\u00a0Hong-Ming\u00a0Yin,\u00a0<em>Determination of the leading coefficient\u00a0a<\/em>(<em>x<\/em>)\u00a0<em>in the heat equation\u00a0u<\/em><sub><em>t<\/em><\/sub>\u00a0=\u00a0<em>a<\/em>(<em>x<\/em>)\u0394<em>u<\/em>, Quarterly of Applied Mathematics\u00a0<strong>51\u00a0<\/strong>(1993), no.\u00a03, 577\u2013583, \u00a0<a href=\"http:\/\/doi.org\/10.1090\/qam\/1233531\">http:\/\/doi.org\/10.1090\/qam\/1233531<\/a>.<br>[18]\u00a0Bei\u00a0Hu,\u00a0<em>Nonexistence of a positive solution of the Laplace equation with a nonlinear boundary condition<\/em>, Differential and Integral Equations\u00a0<strong>7\u00a0<\/strong>(1994), no.\u00a02, 301\u2013313.\u00a0<a href=\"https:\/\/projecteuclid.org\/journals\/differential-and-integral-equations\/volume-7\/issue-2\/Nonexistence-of-a-positive-solution-of-the-Laplace-equation-with\/die\/1369330430.full\">https:\/\/projecteuclid.org\/journals\/differential-and-integral-equations\/volume-7\/issue-2\/Nonexistence-of-a-positive-solution-of-the-Laplace-equation-with\/die\/1369330430.full<\/a>.<br>[19]\u00a0Bei\u00a0Hu and\u00a0Hong-Ming\u00a0Yin,\u00a0<em>Global solutions and quenching to a class of quasilinear parabolic equations<\/em>, Forum Mathematicum\u00a0<strong>6\u00a0<\/strong>(1994), no.\u00a03, 371\u2013383, \u00a0<a href=\"http:\/\/doi.org\/10.1515\/form.1994.6.371\">http:\/\/doi.org\/10.1515\/form.1994.6.371<\/a>.<br>[20]\u00a0Bei\u00a0Hu and\u00a0Hong-Ming\u00a0Yin,\u00a0<em>The profile near blowup time for solution of the heat equation with a nonlinear boundary condition<\/em>, Transactions of the American Mathematical Society\u00a0<strong>346<\/strong>\u00a0(1994), no.\u00a01, 117\u2013135, \u00a0<a href=\"http:\/\/doi.org\/10.2307\/2154944\">http:\/\/doi.org\/10.2307\/2154944<\/a>.<br>[21]\u00a0Bei\u00a0Hu and\u00a0Hong-Ming\u00a0Yin,\u00a0<em>Blowup of solution for the heat equation with a nonlinear boundary condition<\/em>, Comparison methods and stability theory, Lecture Notes in Pure and Appl. Mathematical, vol.\u00a0162, Dekker, New York, 1994, pp.\u00a0189\u2013198, \u00a0<a href=\"http:\/\/doi.org\/10.1201\/9781003072140-15\">http:\/\/doi.org\/10.1201\/9781003072140-15<\/a>.<br>[22]\u00a0Bei\u00a0Hu,\u00a0<em>A free boundary problem arising in smoulder combustion<\/em>, Journal of Partial Differential Equations\u00a0<strong>7\u00a0<\/strong>(1994), no.\u00a03, 193\u2013214.\u00a0<a href=\"https:\/\/www.global-sci.org\/intro\/article_detail\/jpde\/5682.html\">https:\/\/www.global-sci.org\/intro\/article_detail\/jpde\/5682.html<\/a>.<br>[23]\u00a0Bei\u00a0Hu,\u00a0<em>Nondegeneracy and single-point-blowup for solution of the heat equation with a nonlinear boundary condition<\/em>, Journal of Mathematical Science, The University of Tokyo\u00a0<strong>1\u00a0<\/strong>(1994), no.\u00a02, 251\u2013276.\u00a0<a href=\"https:\/\/www.ms.u-tokyo.ac.jp\/journal\/abstract_e\/jms010201_e.html\">https:\/\/www.ms.u-tokyo.ac.jp\/journal\/abstract_e\/jms010201_e.html<\/a>.<br>[24]\u00a0Bei\u00a0Hu and\u00a0Jianhua\u00a0Zhang,\u00a0<em>A free boundary problem arising in the modelling of internal oxidation of binary alloys<\/em>, European Journal of Applied Mathematics\u00a0<strong>6\u00a0<\/strong>(1995), no.\u00a03, 225\u2013245, \u00a0<a href=\"http:\/\/doi.org\/10.1017\/S0956792500001819\">http:\/\/doi.org\/10.1017\/S0956792500001819<\/a>.<br>[25]\u00a0Bei\u00a0Hu and\u00a0Jiongmin\u00a0Yong,\u00a0<em>Pontryagin maximum principle for semilinear and quasilinear parabolic equations with pointwise state constraints<\/em>, SIAM Journal on Control Optimization\u00a0<strong>33\u00a0<\/strong>(1995), no.\u00a06, 1857\u20131880, \u00a0<a href=\"http:\/\/doi.org\/10.1137\/S0363012993250074\">http:\/\/doi.org\/10.1137\/S0363012993250074<\/a>.<br>[26]\u00a0Bei\u00a0Hu and\u00a0Hong-Ming\u00a0Yin,\u00a0<em>Semilinear parabolic equations with prescribed energy<\/em>, Rendicenti del Circolo Matematico di Palermo (2)\u00a0<strong>44\u00a0<\/strong>(1995), no.\u00a03, 479\u2013505, \u00a0<a href=\"http:\/\/doi.org\/10.1007\/BF02844682\">http:\/\/doi.org\/10.1007\/BF02844682<\/a>.<br>[27]\u00a0Bei\u00a0Hu and\u00a0Jianhua\u00a0Zhang,\u00a0<em>Global existence for a class of non-Fickian polymer-penetrant systems<\/em>, Journal of Partial Differential Equations\u00a0<strong>9\u00a0<\/strong>(1996), no.\u00a03, 193\u2013208.\u00a0<a href=\"https:\/\/global-sci.org\/intro\/article_detail\/jpde\/5621.html\">https:\/\/global-sci.org\/intro\/article_detail\/jpde\/5621.html<\/a>.<br>[28]\u00a0Avner\u00a0Friedman and\u00a0Bei\u00a0Hu,\u00a0<em>A Stefan problem for multidimensional reaction-diffusion systems<\/em>, SIAM Journal on Mathematical Analysis\u00a0<strong>27\u00a0<\/strong>(1996), no.\u00a05, 1212\u20131234, \u00a0<a href=\"http:\/\/doi.org\/10.1137\/S0036141094272848\">http:\/\/doi.org\/10.1137\/S0036141094272848<\/a>.<br>[29]\u00a0Bei\u00a0Hu and\u00a0Hong-Ming\u00a0Yin,\u00a0<em>On critical exponents for the heat equation with a nonlinear boundary condition<\/em>, Analyse Non Lineaire &#8211; Annales de l\u2018Institut Henri Poincar\u00e9\u00a0<strong>13\u00a0<\/strong>(1996), no.\u00a06, 707\u2013732, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/S0294-1449(16)30120-2\">http:\/\/doi.org\/10.1016\/S0294-1449(16)30120-2<\/a>.<br>[30]\u00a0Bei\u00a0Hu and\u00a0Hong-Ming\u00a0Yin,\u00a0<em>Critical exponents for a system of heat equations coupled in a non-linear boundary condition<\/em>, Mathematical Methods in the Applied Sciences\u00a0<strong>19\u00a0<\/strong>(1996), no.\u00a014, 1099\u20131120, \u00a0<a>3.0.CO;2-J&#8221; &gt;http:\/\/doi.org\/10.1002\/(SICI)1099-1476(19960925)19:14\u00a11099::AID-MMA780\u00bf3.0.CO;2-J<\/a>.<br>[31]\u00a0Bei\u00a0Hu,\u00a0<em>Remarks on the blowup estimate for solution of the heat equation with a nonlinear boundary condition<\/em>, Differential and Integral Equations\u00a0<strong>9\u00a0<\/strong>(1996), no.\u00a05, 891\u2013901.\u00a0<a href=\"https:\/\/projecteuclid.org\/journals\/differential-and-integral-equations\/volume-9\/issue-5\/Remarks-on-the-blowup-estimate-for-solution-of-the-heat\/die\/1367871522.full\">https:\/\/projecteuclid.org\/journals\/differential-and-integral-equations\/volume-9\/issue-5\/Remarks-on-the-blowup-estimate-for-solution-of-the-heat\/die\/1367871522.full<\/a>.<br>[32]\u00a0Bei\u00a0Hu and\u00a0Hong-Ming\u00a0Yin,\u00a0<em>The DeGiorgi-Nash-Moser type of estimate for parabolic Volterra integrodifferential equations<\/em>, Pacific Journal of Mathematics\u00a0<strong>178\u00a0<\/strong>(1997), no.\u00a02, 265\u2013277, \u00a0<a href=\"http:\/\/doi.org\/10.2140\/pjm.1997.178.265\">http:\/\/doi.org\/10.2140\/pjm.1997.178.265<\/a>.<br>[33]\u00a0Jong-Shenq\u00a0Guo and\u00a0Bei\u00a0Hu,\u00a0<em>The profile near quenching time for the solution of a singular semilinear heat equation<\/em>, Proceedings of the Edinburgh Mathematical Society (2)\u00a0<strong>40\u00a0<\/strong>(1997), no.\u00a03, 437\u2013456, \u00a0<a href=\"http:\/\/doi.org\/10.1017\/S0013091500023932\">http:\/\/doi.org\/10.1017\/S0013091500023932<\/a>.<br>[34]\u00a0Avner\u00a0Friedman\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Head-media interaction in magnetic recording<\/em>, Archive for Rational Mechanics and Analysis\u00a0<strong>140\u00a0<\/strong>(1997), no.\u00a01, 79\u2013101, \u00a0<a href=\"http:\/\/doi.org\/10.1007\/s002050050061\">http:\/\/doi.org\/10.1007\/s002050050061<\/a>.<br>[35]\u00a0Bei\u00a0Hu and\u00a0Hong-Ming\u00a0Yin,\u00a0<em>On critical exponents for the heat equation with a mixed nonlinear Dirichlet-Neumann boundary condition<\/em>, Journal of Mathematical Analysis and Applications\u00a0<strong>209\u00a0<\/strong>(1997), no.\u00a02, 683\u2013711, \u00a0<a href=\"http:\/\/doi.org\/10.1006\/jmaa.1997.5397\">http:\/\/doi.org\/10.1006\/jmaa.1997.5397<\/a>.<br>[36]\u00a0Avner\u00a0Friedman, Bei\u00a0Hu,\u00a0and\u00a0Yong\u00a0Liu,\u00a0<em>A boundary value problem for the Poisson equation with multi-scale oscillating boundary<\/em>, Journal of Differential Equations\u00a0<strong>137\u00a0<\/strong>(1997), no.\u00a01, 54\u201393, \u00a0<a href=\"http:\/\/doi.org\/10.1006\/JDEQ.1997.3257\">http:\/\/doi.org\/10.1006\/JDEQ.1997.3257<\/a>.<br>[37]\u00a0Avner\u00a0Friedman and\u00a0Bei\u00a0Hu,\u00a0<em>A non-stationary multi-scale oscillating free boundary for the Laplace and heat equations<\/em>, Journal of Differential Equations\u00a0<strong>137\u00a0<\/strong>(1997), no.\u00a01, 119\u2013165, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/S0022-0396(06)80006-9\">http:\/\/doi.org\/10.1016\/S0022-0396(06)80006-9<\/a>.<br>[38]\u00a0Avner\u00a0Friedman and\u00a0Bei\u00a0Hu,\u00a0<em>Optimal control of a chemical vapor deposition reactor<\/em>, Journal of Optimization Theory and Applications\u00a0<strong>97\u00a0<\/strong>(1998), no.\u00a03, 623\u2013644, \u00a0<a href=\"http:\/\/doi.org\/10.1023\/A:1022694210246\">http:\/\/doi.org\/10.1023\/A:1022694210246<\/a>.<br>[39]\u00a0Avner\u00a0Friedman, Bei\u00a0Hu,\u00a0and\u00a0J. J. L. Velazquez,\u00a0<em>Asymptotics for the biharmonic equation near the tip of a crack<\/em>, Indiana University Mathematics Journal\u00a0<strong>47\u00a0<\/strong>(1998), no.\u00a04, 1327\u20131395.\u00a0<a href=\"https:\/\/www.jstor.org\/stable\/24900069\">https:\/\/www.jstor.org\/stable\/24900069<\/a>.<br>[40]\u00a0Avner\u00a0Friedman and\u00a0Bei\u00a0Hu,\u00a0<em>A Stefan problem for a protocell model<\/em>, SIAM Journal on Mathematical Analysis\u00a0<strong>30<\/strong>\u00a0(1999), no.\u00a04, 912\u2013926, \u00a0<a href=\"http:\/\/doi.org\/10.1137\/S0036141098337588\">http:\/\/doi.org\/10.1137\/S0036141098337588<\/a>.<br>[41]\u00a0Jong-Shenq\u00a0Guo and\u00a0Bei\u00a0Hu,\u00a0<em>Quenching profile for a quasilinear parabolic equation<\/em>, Quarterly of Applied Mathematics\u00a0<strong>58\u00a0<\/strong>(2000), no.\u00a04, 613\u2013626.\u00a0<a href=\"https:\/\/www.jstor.org\/stable\/43638503\">https:\/\/www.jstor.org\/stable\/43638503<\/a>.<br>[42]\u00a0Avner\u00a0Friedman, Bei\u00a0Hu,\u00a0and\u00a0J. J. L. Velazquez,\u00a0<em>The evolution of stress intensity factors and the propagation of cracks in elastic media<\/em>, Archive for Rational Mechanics and Analysis\u00a0<strong>152\u00a0<\/strong>(2000), no.\u00a02, 103\u2013139, \u00a0<a href=\"http:\/\/doi.org\/10.1007\/s002050000072\">http:\/\/doi.org\/10.1007\/s002050000072<\/a>.<br>[43]\u00a0Avner\u00a0Friedman, Bei\u00a0Hu,\u00a0and\u00a0J. J. L. Velazquez,\u00a0<em>On the zeros of quotients of Bessel functions<\/em>, Chinese Annals of Mathematics, Ser. B\u00a0<strong>21\u00a0<\/strong>(2000), no.\u00a03, 285\u2013296, \u00a0<a href=\"http:\/\/doi.org\/10.1142\/S0252959900000315\">http:\/\/doi.org\/10.1142\/S0252959900000315<\/a>.<br>[44]\u00a0Avner\u00a0Friedman, Bei\u00a0Hu,\u00a0and\u00a0J. J. L. Velazquez,\u00a0<em>The evolution of stress intensity factors in the propagation of two dimensional cracks<\/em>, European Journal of Applied Mathematics\u00a0<strong>11\u00a0<\/strong>(2000), no.\u00a05, 453\u2013471, \u00a0<a href=\"http:\/\/doi.org\/10.1017\/S0956792500004265\">http:\/\/doi.org\/10.1017\/S0956792500004265<\/a>.<br>[45]\u00a0Avner\u00a0Friedman, Bei\u00a0Hu,\u00a0and\u00a0J. J. L. Velazquez,\u00a0<em>A Stefan problem for a protocell model with symmetry-breaking bifurcations of analytic solutions<\/em>, Interfaces and Free Boundaries\u00a0<strong>3<\/strong>\u00a0(2001), no.\u00a02, 143\u2013199, \u00a0<a href=\"http:\/\/doi.org\/10.4171\/IFB\/37\">http:\/\/doi.org\/10.4171\/IFB\/37<\/a>.<br>[46]\u00a0Jong-Shenq\u00a0Guo and\u00a0Bei\u00a0Hu,\u00a0<em>Blowup rate for heat equation in Lipschitz domains with nonlinear heat source terms on the boundary<\/em>, Journal of Mathematical Analysis and Applications\u00a0<strong>269\u00a0<\/strong>(2002), no.\u00a01, 28\u201349, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/S0022-247X(02)00002-1\">http:\/\/doi.org\/10.1016\/S0022-247X(02)00002-1<\/a>.<br>[47]\u00a0Marco\u00a0A. Fontelos, Avner\u00a0Friedman,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Mathematical analysis of a model for the initiation of angiogenesis<\/em>, SIAM Journal on Mathematical Analysis\u00a0<strong>33\u00a0<\/strong>(2002), no.\u00a06, 1330\u20131355, \u00a0<a href=\"http:\/\/doi.org\/10.1137\/S0036141001385046\">http:\/\/doi.org\/10.1137\/S0036141001385046<\/a>.<br>[48]\u00a0Jong-Shenq\u00a0Guo and\u00a0Bei\u00a0Hu,\u00a0<em>Blowup behavior for a nonlinear parabolic equation of nondivergence form<\/em>, Nonlinear Analysis: Theory, Method and Application\u00a0<strong>61\u00a0<\/strong>(2005), no.\u00a04, 577\u2013590, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.na.2005.01.022\">http:\/\/doi.org\/10.1016\/j.na.2005.01.022<\/a>.<br>[49]\u00a0Bei\u00a0Hu and\u00a0David\u00a0P. 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Bazaliy, Ya. B. 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Series A\u00a0<strong>20\u00a0<\/strong>(2008), no.\u00a04, 927-937, \u00a0<a href=\"http:\/\/doi.org\/10.3934\/DCDS.2008.20.927\">http:\/\/doi.org\/10.3934\/DCDS.2008.20.927<\/a>.<br>[60]\u00a0Avner\u00a0Friedman and\u00a0Bei\u00a0Hu,\u00a0<em>Stability and instability of Liapounov-Schmidt and Hopf bifurcation for a free boundary problem arising in a tumor model<\/em>, Transactions of the American Mathematical Society\u00a0<strong>360<\/strong>\u00a0(2008), no.\u00a010, 5291-5342, \u00a0<a href=\"http:\/\/doi.org\/10.1090\/S0002-9947-08-04468-1\">http:\/\/doi.org\/10.1090\/S0002-9947-08-04468-1<\/a>.<br>[61]\u00a0Xinfu\u00a0Chen, Avner\u00a0Friedman,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>A Parabolic\u2013Hyperbolic Quasilinear System<\/em>, Communications in Partial Differential Equations\u00a0<strong>33\u00a0<\/strong>(2008), no.\u00a06, 969\u2013987, \u00a0<a href=\"http:\/\/doi.org\/10.1080\/03605300701588714\">http:\/\/doi.org\/10.1080\/03605300701588714<\/a>.<br>[62]\u00a0Avner\u00a0Friedman and\u00a0Bei\u00a0Hu,\u00a0<em>The role of oxygen in tissue maintenance: a mathematical model<\/em>, Mathematical Models and Methods in Applied Sciences\u00a0<strong>18\u00a0<\/strong>(2008), no.\u00a08, 1409\u20131441, \u00a0<a href=\"http:\/\/doi.org\/10.1142\/S021820250800308X\">http:\/\/doi.org\/10.1142\/S021820250800308X<\/a>.<br>[63]\u00a0Xinfu\u00a0Chen and\u00a0Bei\u00a0Hu,\u00a0<em>Viscosity solutions of a discontinuous Hamilton-Jacobi equation<\/em>, Interfaces and Free boundaries\u00a0<strong>10\u00a0<\/strong>(2008), no.\u00a03, 339\u2013359, \u00a0<a href=\"http:\/\/doi.org\/10.4171\/IFB\/192\">http:\/\/doi.org\/10.4171\/IFB\/192<\/a>.<br>[64]\u00a0Hua\u00a0Zhang, Changzhen\u00a0Qu,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Bifurcation for a free boundary problem modeling a protocell<\/em>, Nonlinear Analysis, Theory, Method and Application\u00a0<strong>70\u00a0<\/strong>(2009), 2779\u20132795, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.na.2008.04.003\">http:\/\/doi.org\/10.1016\/j.na.2008.04.003<\/a>.<br>[65]\u00a0Bei\u00a0Hu, Lishang\u00a0Jiang,\u00a0and\u00a0Jin\u00a0Liang,\u00a0<em>Optimal convergence rate of the Binomial Tree Scheme for American options<\/em>, Journal of Computational and Applied Mathematics\u00a0<strong>230\u00a0<\/strong>(2009), 583\u2013599, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.cam.2008.12.018\">http:\/\/doi.org\/10.1016\/j.cam.2008.12.018<\/a>.<br>[66]\u00a0Jong-Shenq\u00a0Guo, Bei\u00a0Hu,\u00a0and\u00a0Chi-Jen\u00a0Wang,\u00a0<em>A nonlocal quenching problem arising in micro-electro mechanical system<\/em>, Quarterly of Applied Mathematics\u00a0<strong>67\u00a0<\/strong>(2009), no.\u00a04, 725\u2013734.<br>[67]\u00a0Avner\u00a0Friedman, Bei\u00a0Hu,\u00a0and\u00a0Chiu-Yen\u00a0Kao,\u00a0<em>Cell cycle control at the first restriction point and its effect on tissue growth<\/em>, Journal of Mathematical Biology\u00a0<strong>60\u00a0<\/strong>(2010), 881\u2013907, \u00a0<a href=\"http:\/\/doi.org\/10.1007\/s00285-009-0290-7\">http:\/\/doi.org\/10.1007\/s00285-009-0290-7<\/a>.<br>[68]\u00a0Zhengce\u00a0Zhang and\u00a0Bei\u00a0Hu,\u00a0<em>Gradient blowup rate for a semilinear parabolic equation<\/em>, Discrete and Continuous Dynamical Systems &#8211; 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Hauenstein, Bei\u00a0Hu, Yuan\u00a0Liu, Andrew\u00a0J. Sommese,\u00a0and\u00a0Yong-Tao\u00a0Zhang,\u00a0<em>Multiple stable steady states of a reaction-diffusion model on zebrafish dorsal-ventral patterning<\/em>, Discrete and Continuous Dynamical Systems &#8211; Series S\u00a0<strong>4\u00a0<\/strong>(2011), no.\u00a06, 1413\u20131428, \u00a0<a href=\"http:\/\/doi.org\/10.3934\/dcdss.2011.4.1413\">http:\/\/doi.org\/10.3934\/dcdss.2011.4.1413<\/a>.<br>[74]\u00a0Wenrui\u00a0Hao, Jonathan\u00a0D. Hauenstein, Bei\u00a0Hu,\u00a0and\u00a0Andrew\u00a0J. Sommese,\u00a0<em>A three-dimensional steady-state tumor system<\/em>, Applied Mathematics and Computation\u00a0<strong>218<\/strong>\u00a0(2011), no.\u00a06, 2661\u20132669, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.amc.2011.08.006\">http:\/\/doi.org\/10.1016\/j.amc.2011.08.006<\/a>.<br>[75]\u00a0Wenrui\u00a0Hao, Jonathan\u00a0D. Hauenstein, Bei\u00a0Hu, Yuan\u00a0Liu, Andrew\u00a0J. 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\u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.jde.2015.02.002\">http:\/\/doi.org\/10.1016\/j.jde.2015.02.002<\/a>.<br>[88]\u00a0Xinfu\u00a0Chen, Bei\u00a0Hu, Jin\u00a0Liang,\u00a0and\u00a0Yajing\u00a0Zhang,\u00a0<em>Convergence rate of free boundary of numerical scheme for America option<\/em>, Discrete and Continuous Dynamical Systems, Ser.\u00a0B\u00a0<strong>21\u00a0<\/strong>(2016), no.\u00a0 5, 1435\u20131444, \u00a0<a href=\"http:\/\/doi.org\/10.3934\/dcdsb.2016004\">http:\/\/doi.org\/10.3934\/dcdsb.2016004<\/a>.<br>[89]\u00a0Jin\u00a0Liang, Yuan\u00a0Wu,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Asymptotic traveling wave solution for a credit rating migration problem<\/em>, Journal of Differential Equations\u00a0<strong>261\u00a0<\/strong>(2016), 1017\u20131045, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.jde.2016.03.032\">http:\/\/doi.org\/10.1016\/j.jde.2016.03.032<\/a>.<br>[90]\u00a0Yaodan\u00a0Huang, Zhengce\u00a0Zhang,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Bifurcation for a free-boundary tumor model with angiogenesis<\/em>, Nonlinear Analysis: Real World Applications\u00a0<strong>35\u00a0<\/strong>(2017), 483\u2013502, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.nonrwa.2016.12.003\">http:\/\/doi.org\/10.1016\/j.nonrwa.2016.12.003<\/a>.<br>[91]\u00a0Xiaoli\u00a0Yang, Jin\u00a0Liang,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Minimization of carbon abatement cost: modeling, analysis and simulation<\/em>, Discrete and Continuous Dynamical Systems, Ser.\u00a0B\u00a0<strong>22\u00a0<\/strong>(2017), no.\u00a0 7, 2939\u20132969, \u00a0<a href=\"http:\/\/doi.org\/10.3934\/dcdsb.2017158\">http:\/\/doi.org\/10.3934\/dcdsb.2017158<\/a>.<br>[92]\u00a0Jongshenq\u00a0Guo and\u00a0Bei\u00a0Hu,\u00a0<em>Quenching rate for a nonlocal problem arising in the micro-electro mechanical system<\/em>, Journal of Differential Equations\u00a0<strong>264\u00a0<\/strong>(2018), 3285-3311, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.jde.2017.11.017\">http:\/\/doi.org\/10.1016\/j.jde.2017.11.017<\/a>.<br>[93]\u00a0Wenrui\u00a0Hao, Bei\u00a0Hu, Shuwang\u00a0Li,\u00a0and\u00a0Lingyu\u00a0Song,\u00a0<em>Convergence of boundary integral method for a free boundary system<\/em>, Journal of Computational and Applied Mathematics\u00a0<strong>334<\/strong>\u00a0(2018), 128\u2013157, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.cam.2017.11.016\">http:\/\/doi.org\/10.1016\/j.cam.2017.11.016<\/a>.<br>[94]\u00a0Hongjing\u00a0Pan, Ruixiang\u00a0Xing,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>A free boundary problem with two moving boundaries modeling grain hydration<\/em>, Nonlinearity\u00a0<strong>31\u00a0<\/strong>(2018), 3591\u20133616, \u00a0<a href=\"http:\/\/doi.org\/10.1088\/1361-6544\/aabf04\">http:\/\/doi.org\/10.1088\/1361-6544\/aabf04<\/a>.<br>[95]\u00a0Yan\u00a0Li, Zhengce\u00a0Zhang,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Convergence rate of an explicit finite difference scheme for a credit rating migration problem<\/em>, SIAM Journal on Numerical Analysis\u00a0<strong>56\u00a0<\/strong>(2018), no.\u00a0 4, 2430\u20132460, \u00a0<a href=\"http:\/\/doi.org\/10.1137\/17M1151833\">http:\/\/doi.org\/10.1137\/17M1151833<\/a>.<br>[96]\u00a0Yaodan\u00a0Huang, Zhengce\u00a0Zhang,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Bifurcation from stability to instability for a free-boundary tumor model with angiogenesis<\/em>, Discrete and Continuous Dynamical Systems, Ser.\u00a0A\u00a0<strong>39\u00a0<\/strong>(2019), no.\u00a05, 2473\u20132510.<br>[97]\u00a0Yaodan\u00a0Huang, Zhengce\u00a0Zhang,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Linear stability for a free-boundary tumor model with a periodic supply of external nutrients<\/em>, Mathematical Methods in Applied Sciences\u00a0<strong>42\u00a0<\/strong>(2019), 1039\u20131054, \u00a0<a href=\"http:\/\/doi.org\/10.1002\/MMA.5412\">http:\/\/doi.org\/10.1002\/MMA.5412<\/a>.<br>[98]\u00a0Rui\u00a0Li and\u00a0Bei\u00a0Hu,\u00a0<em>A parabolic-hyperbolic system modeling the growth of a tumor<\/em>, Journal of Differential Equations\u00a0<strong>267\u00a0<\/strong>(2019), 693\u2013741, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.jde.2019.01.020\">http:\/\/doi.org\/10.1016\/j.jde.2019.01.020<\/a>.<br>[99]\u00a0Yuan\u00a0Wu, Jin\u00a0Liang,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>A free boundary problem for defaultable corporate bond with credit rating migration risk and its asymptotic behavior<\/em>, Discrete and Continuous Dynamical Systems, Ser.\u00a0B\u00a0<strong>25\u00a0<\/strong>(2020), no.\u00a03, 1043\u20131058, \u00a0<a href=\"http:\/\/doi.org\/10.3934\/dcdsb.2019207\">http:\/\/doi.org\/10.3934\/dcdsb.2019207<\/a>.<br>[100]\u00a0Xinyue\u00a0Evelyn\u00a0Zhao and\u00a0Bei\u00a0Hu,\u00a0<em>The impact of time delay in a tumor model<\/em>, Nonlinear Analysis: Real World Applications\u00a0<strong>51\u00a0<\/strong>(2020), 103015 (February), \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.nonrwa.2019.103015\">http:\/\/doi.org\/10.1016\/j.nonrwa.2019.103015<\/a>.<br>[101]\u00a0Xinyue\u00a0Evelyn\u00a0Zhao and\u00a0Bei\u00a0Hu,\u00a0<em>Symmetry-breaking bifurcation for a free-boundary tumor model with time delay<\/em>, Journal of Differential Equations\u00a0<strong>269\u00a0<\/strong>(2020), 1829\u20131862, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.jde.2020.01.022\">http:\/\/doi.org\/10.1016\/j.jde.2020.01.022<\/a>.<br>[102]\u00a0Junfan\u00a0Lu and\u00a0Bei\u00a0Hu,\u00a0<em>Bifurcation for a free boundary problem modeling the growth of multi-layer tumors with ECM and MDE interactions<\/em>, Mathematical Methods in Applied Sciences\u00a0<strong>43\u00a0<\/strong>(2020), 3617\u20133636, \u00a0<a href=\"http:\/\/doi.org\/10.1002\/mma.6142\">http:\/\/doi.org\/10.1002\/mma.6142<\/a>.<br>[103]\u00a0Bei\u00a0Hu and\u00a0Youshan\u00a0Tao,\u00a0<em>Critical mass of lymphocytes for the coexistence in a chemotaxis system modeling tumor-immune cell interactions<\/em>, Zeitschrift f\u00fcr Angewandte Mathematik und Physik\u00a0<strong>71\u00a0<\/strong>(2020), 5, \u00a0<a href=\"http:\/\/doi.org\/10.1007\/s00033-020-01405-6\">http:\/\/doi.org\/10.1007\/s00033-020-01405-6\u00a0<\/a>.<br>[104]\u00a0Yaodan\u00a0Huang, Zhengce\u00a0Zhang,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Asymptotic stability for a free boundary tumor model with angiogenesis<\/em>, Journal of Differential Equations\u00a0<strong>270\u00a0<\/strong>(2021), no.\u00a0 167, 961\u2013993, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.jde.2020.08.050\">http:\/\/doi.org\/10.1016\/j.jde.2020.08.050\u00a0<\/a>.<br>[105]\u00a0Huijuan\u00a0Song, Bei\u00a0Hu,\u00a0and\u00a0Zejia\u00a0Wang,\u00a0<em>Stationary solutions of a free boundary problem modeling the growth of necrotic tumors with angiogenesis<\/em>, Discrete and Continuous Dynamical Systems, Ser.\u00a0B\u00a0<strong>\u00a0261\u00a0<\/strong>(2021), 667\u2013691, \u00a0<a href=\"http:\/\/doi.org\/10.3934\/dcdsb.2020084\">http:\/\/doi.org\/10.3934\/dcdsb.2020084<\/a>.<br>[106]\u00a0Xinyue\u00a0Evelyn\u00a0Zhao and\u00a0Bei\u00a0Hu,\u00a0<em>Bifurcation for a free boundary problem modeling a small arterial plaque<\/em>, Journal of Differential Equations\u00a0<strong>288\u00a0<\/strong>(2021), 250\u2013287, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.jde.2021.04.008\">http:\/\/doi.org\/10.1016\/j.jde.2021.04.008<\/a>.<br>[107]\u00a0Xinyue\u00a0Evelyn\u00a0Zhao, Wenrui\u00a0Hao,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Convergence analysis of neural networks for solving a free boundary system<\/em>, Computers and Mathematics with Applications\u00a0<strong>93\u00a0<\/strong>(2021), 144\u2013155, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.camwa.2021.03.032\">http:\/\/doi.org\/10.1016\/j.camwa.2021.03.032<\/a>.<br>[108]\u00a0Xinyue\u00a0Evelyn\u00a0Zhao and\u00a0Bei\u00a0Hu,\u00a0<em>On the first bifurcation point for a free boundary problem modeling a small arterial plaque<\/em>, Mathematical Methods in the Applied Sciences\u00a0<strong>45\u00a0<\/strong>(2022), no.\u00a09, 4974\u20134988, \u00a0<a href=\"http:\/\/doi.org\/10.1002\/mma.8087\">http:\/\/doi.org\/10.1002\/mma.8087<\/a>.<br>[109]\u00a0Wenhua\u00a0He, Ruixiang\u00a0Xing,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Linear stability analysis for a free boundary problem modeling multi-layer tumor growth with time delay<\/em>, SIAM Journal on Mathematical Analysis\u00a0<strong>54\u00a0<\/strong>(2022), no.\u00a04, 4238\u20134276, \u00a0<a href=\"http:\/\/doi.org\/10.1137\/21M1437494\">http:\/\/doi.org\/10.1137\/21M1437494<\/a>.<br>[110]\u00a0Wenhua\u00a0He, Ruixiang\u00a0Xing,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>The linear stability for a free boundary problem modeling multi-layer tumor growth with time delay<\/em>, Mathematical Methods in the Applied Sciences\u00a0<strong>45\u00a0<\/strong>(2022), no.\u00a011, 7096\u20137118, \u00a0<a href=\"http:\/\/doi.org\/10.1002\/mma.8227\">http:\/\/doi.org\/10.1002\/mma.8227<\/a>.<br>[111]\u00a0Heqian\u00a0Lu, Bei\u00a0Hu,\u00a0and\u00a0Zhengce\u00a0Zhang,\u00a0<em>Blowup time estimates for the heat equation with a nonlocal boundary condition<\/em>, Zeitschrift f\u00fcr Angewandte Mathematik und Physik\u00a0<strong>73<\/strong>\u00a0(2022), Article 60, \u00a0<a href=\"http:\/\/doi.org\/10.1007\/s00033-022-01698-9\">http:\/\/doi.org\/10.1007\/s00033-022-01698-9<\/a>.<br>[112]\u00a0Caihong\u00a0Chang, Bei\u00a0Hu,\u00a0and\u00a0Zhengce\u00a0Zhang,\u00a0<em>Liouville-type theorems and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms<\/em>, Nonlinear Analysis: Theory, Method and Application\u00a0<strong>220\u00a0<\/strong>(2022), Article 112873, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.na.2022.112873\">http:\/\/doi.org\/10.1016\/j.na.2022.112873<\/a>.<br>[113]\u00a0Xinyue\u00a0Evelyn\u00a0Zhao, Wenrui\u00a0Hao,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Two neural-network-based methods for solving elliptic obstacle problems<\/em>, Chaos, Solitons and Fractals: the Interdisciplinary Journal of Nonlinear Science\u00a0<strong>161\u00a0<\/strong>(2022), 112313, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.chaos.2022.112313\">http:\/\/doi.org\/10.1016\/j.chaos.2022.112313<\/a>.<br>[114]\u00a0Yaodan\u00a0Huang and\u00a0Bei\u00a0Hu,\u00a0<em>Symmetry-breaking longitude bifurcations for a free boundary problem modeling small plaques in three dimensions<\/em>, Journal of Mathematical Biology\u00a0<strong>\u00a085<\/strong>\u00a0(2022), no.\u00a05, Article 58, \u00a0<a href=\"http:\/\/doi.org\/10.1007\/s00285-022-01827-y\">http:\/\/doi.org\/10.1007\/s00285-022-01827-y<\/a>.<br>[115]\u00a0Xiaohong\u00a0Zhang, Bei\u00a0Hu,\u00a0and\u00a0Zhengce\u00a0Zhang,\u00a0<em>A three-dimensional angiogenesis model with time-delay<\/em>, Discrete and Continuous Dynamical Systems, Ser.\u00a0B\u00a0<strong>\u00a028\u00a0<\/strong>(2023), no.\u00a03, 1823 \u2013 1854, \u00a0<a href=\"http:\/\/doi.org\/10.3934\/dcdsb.2022149\">http:\/\/doi.org\/10.3934\/dcdsb.2022149<\/a>.<br>[116]\u00a0Xiaohong\u00a0Zhang, Bei\u00a0Hu,\u00a0and\u00a0Zhengce\u00a0Zhang,\u00a0<em>Bifurcation for a free-boundary problem modeling small plaques with reverse cholesterol transport<\/em>, Journal of Mathematical Analysis and Application\u00a0<strong>\u00a0517\u00a0<\/strong>(2023), Article 126604, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.jmaa.2022.126604\">http:\/\/doi.org\/10.1016\/j.jmaa.2022.126604<\/a>.<br>[117]\u00a0Min-Jhe\u00a0Lu,\u00a0Wenrui\u00a0Hao, Bei\u00a0Hu,\u00a0and\u00a0Shuwang\u00a0Li,\u00a0<em>Bifurcation analysis of a free boundary model of vascular tumor growth with a necrotic core and chemotaxis<\/em>, Journal of Mathematical Biology\u00a0<strong>\u00a086\u00a0<\/strong>(2023), no.\u00a01, Article 19, \u00a0<a href=\"http:\/\/doi.org\/10.1007\/s00285-022-01862-9\">http:\/\/doi.org\/10.1007\/s00285-022-01862-9<\/a>.<br>[118]\u00a0Caihong\u00a0Chang, Bei\u00a0Hu,\u00a0and\u00a0Zhengce\u00a0Zhang,\u00a0<em>Gradient blowup behavior for a viscous Hamilton-Jacobi equation with degenerate gradient nonlinearity<\/em>, Journal of Differential Equations\u00a0<strong>\u00a0359\u00a0<\/strong>(2023), 23\u201366, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.jde.2023.02.030\">http:\/\/doi.org\/10.1016\/j.jde.2023.02.030<\/a>.<br>[119]\u00a0Yaodan\u00a0Huang and\u00a0Bei\u00a0Hu,\u00a0<em>Periodic solution for a free boundary problem modeling small plaques<\/em>, Communications in Information and Systems\u00a0<strong>23\u00a0<\/strong>(2023), no.\u00a03, 263\u2013287, \u00a0<a href=\"http:\/\/doi.org\/10.4310\/CIS.2023.v23.n3.a3\">http:\/\/doi.org\/10.4310\/CIS.2023.v23.n3.a3<\/a>.<br>[120]\u00a0Xinfu\u00a0Chen, Bei\u00a0Hu, Jin\u00a0Liang,\u00a0and\u00a0Hongming\u00a0Yin,\u00a0<em>The free boundary problem for measuring credit rating migration risks (in Chinese)<\/em>, Scientia Sinica Mathematica\u00a0<strong>\u00a054\u00a0<\/strong>(2024), no.\u00a03, 285\u2013312, \u00a0<a href=\"http:\/\/doi.org\/10.1360\/SSM-2022-0151\">http:\/\/doi.org\/10.1360\/SSM-2022-0151<\/a>.<br>[121]\u00a0Yaodan\u00a0Huang and\u00a0Bei\u00a0Hu,\u00a0<em>Symmetry-breaking combined latitude-longitude bifurcations for a free boundary problem modeling small plaques<\/em>, Discrete and Continuous Dynamical Systems, Ser.\u00a0B\u00a0<strong>\u00a029\u00a0<\/strong>(2024), no.\u00a010, 4120\u20134149, \u00a0<a href=\"http:\/\/doi.org\/10.3934\/dcdsb.2024037\">http:\/\/doi.org\/10.3934\/dcdsb.2024037<\/a>.<br>[122]\u00a0Yaodan\u00a0Huang and\u00a0Bei\u00a0Hu,\u00a0<em>Periodic solution for a free-boundary tumor model with small diffusion-to-growth ratio<\/em>, Journal of Differential Equations\u00a0<strong>399\u00a0<\/strong>(2024), 252\u2013280, \u00a0<a href=\"http:\/\/doi.org\/10.1016\/j.jde.2024.03.028\">http:\/\/doi.org\/10.1016\/j.jde.2024.03.028<\/a>.<br>[123]\u00a0Jin\u00a0Liang and\u00a0Bei\u00a0Hu,\u00a0<em>Credit Rating Migration Risks in Structure Models<\/em>, Lecture Notes in Mathematics volume 2018, Springer, 2024, \u00a0<a href=\"http:\/\/doi.org\/10.1007\/978-981-97-2179-5\">http:\/\/doi.org\/10.1007\/978-981-97-2179-5<\/a>.<br>[124]\u00a0Jiangyi\u00a0Liu and\u00a0Bei\u00a0Hu,\u00a0<em>Stability of periodic solution for a free boundary problem modeling small plaques<\/em>, Mathematical Biosciences\u00a0<strong>382\u00a0<\/strong>(2025), Article 109397, \u00a0<a href=\"http:\/\/doi.org\/\/10.1016\/j.mbs.2025.109397\">http:\/\/doi.org\/\/10.1016\/j.mbs.2025.109397<\/a>.<br>[125]\u00a0Jiangyi\u00a0Liu and\u00a0Bei\u00a0Hu,\u00a0<em>Periodic solution for a free boundary Vascular Tumor Model<\/em>, Discrete and Continuous Dynamical Systems, Ser.\u00a0B\u00a0<strong>30\u00a0<\/strong>(2025), no.\u00a012, 5073\u20135093, \u00a0<a href=\"http:\/\/doi.org\/\/10.3934\/dcdsb.2025098\">http:\/\/doi.org\/\/10.3934\/dcdsb.2025098<\/a>.<br>[126]\u00a0Caihong\u00a0Chang, Zhengce\u00a0Zhang,\u00a0and\u00a0Bei\u00a0Hu,\u00a0<em>Analysis of a free boundary problem modeling immune response to fungal infection in multi-space dimensional case<\/em>, Journal of Differential Equations\u00a0<strong>453\u00a0<\/strong>(2026), no.\u00a0part 3, Paper No. 113857, 32, \u00a0<a href=\"http:\/\/doi.org\/\/10.1016\/j.jde.2025.113857\">http:\/\/doi.org\/\/10.1016\/j.jde.2025.113857<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Updated February 12, 2026&nbsp; Book edited[1] Mark Alber, Bei Hu, and Joachim Rosenthal (eds.),&nbsp;Current and future directions in applied mathematics, Birkh\u00e4user Boston Inc., Boston, MA, 1997.&nbsp;http:\/\/doi.org\/10.1007\/978-1-4612-2012-1. Book translated[1]&nbsp;Ya-Zhe&nbsp;Chen and&nbsp;Lan-Cheng&nbsp;Wu,&nbsp;Second order elliptic equations and elliptic systems, translated by Bei Hu, Translations of Mathematical Monographs, vol.&nbsp;174, American Mathematical Society, Providence, RI, 1998.&nbsp;https:\/\/www.ams.org\/books\/mmono\/174\/. Books[1]&nbsp;Bei&nbsp;Hu,&nbsp;Blow-up Theories for Semilinear Parabolic [&hellip;]<\/p>\n","protected":false},"author":2686,"featured_media":0,"parent":268,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.nd.edu\/bei-hu\/wp-json\/wp\/v2\/pages\/2","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.nd.edu\/bei-hu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.nd.edu\/bei-hu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/bei-hu\/wp-json\/wp\/v2\/users\/2686"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/bei-hu\/wp-json\/wp\/v2\/comments?post=2"}],"version-history":[{"count":27,"href":"https:\/\/sites.nd.edu\/bei-hu\/wp-json\/wp\/v2\/pages\/2\/revisions"}],"predecessor-version":[{"id":387,"href":"https:\/\/sites.nd.edu\/bei-hu\/wp-json\/wp\/v2\/pages\/2\/revisions\/387"}],"up":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/bei-hu\/wp-json\/wp\/v2\/pages\/268"}],"wp:attachment":[{"href":"https:\/\/sites.nd.edu\/bei-hu\/wp-json\/wp\/v2\/media?parent=2"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}