**Research Interests:**

I am interested in Partial Differential Equations (PDE) and their applications in Engineering, Industry, and Biology. Many physical processes can be modeled using PDEs.

A mathematical model is an approximation of the real physical phenomenon; it saves time and resources by analyzing the mathematical model rather than the underlying physical world. The physical world is very complicated, therefore, a good mathematical model should not include all the details of the problem, but rather, the model should be simple enough to capture some essential part of the problem and may provide some essential information for the real physical phenomenon.

For the PDE model, we study the properties such as existence, uniqueness, asymptotic behavior, and special properties of the solutions.

We use techniques such as fundamental elliptic and parabolic a priori estimates, fixed point approach, variational argument, energy estimates, numerical computations and computer simulations.

**Current Research:**

PDE elliptic and parabolic a priori estimates, variational inequalities, free boundary problems, reaction-diffusion equations, singular perturbations, asymptotic analysis, homogenization approaches, optimal control in PDE problems, and their applications to industry, Biology and other fields. His current projects include the study of a variety of tumor growth models, thermal runaway that could result in the blowup phenomenon, and partial differential equations from other fields.