偏微分方程理论及其应用/Partial Differential Equations and their Applications

• In particular, I am interested in PDEs and their applications in Geometry, Physical mechanics, Fluid dynamics, Biology, Industry and Engineering, etc. A mathematical model of PDEs is an approximation of the real physical phenomenon for describing certain physical process, and 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 local and global properties such as existence, uniqueness, regularity, asymptotic behavior, formation of singularities, and other special properties of the solutions. We use techniques such as foundamental elliptic and parabolic a priori estimates, fixed point theorems, variational argument, sub- and supersolution method, energy estimates, numerical computations and computer simulations.