**Research Areas:**
Partial Differential Equations;
Mathematical Biology;
Numerical Differential Equations;
Scientific Computing.

**Research Interests:**
I am interested in Partial Differential Equations (PDE) and their applications in Biology
and Engineering. 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 also provide some essential information for the real physical phenomenon.

For PDE models, we study properties such as existence, uniqueness, asymptotic behavior, and their implications.

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

**Current Research:**
Mathematical Biology free boundary problems modeled by PDE, with emphasis on rigorous analysis of the
qualitative behavior of the system. The techniques include PDE elliptic and parabolic a priori estimates,
variational inequalities, bifucation analysis, asymptotic analysis, and numerical simulations.

My past projects also include thermal run away that could result the blowup phenomenon, mathemtical fininace modeled as a PDE free boundary problem, homogenization approaches, optimal control in PDE problems, and their applications to other fields.

**Email:** b1hu@nd.edu
**Office:** 174 Hurley
**Phone:** (574) 631-8630
**Fax:** (574) 631-4822