Title: Multidimensional Shock Waves, Free Boundary Problems and Nonlinear PDEs of Mixed Type
Speaker: Gui-Qiang G. Chen
Speaker Info: Oxford
Special Note: Note unusual day, time, location.
In this talk, we discuss some of the most recent developments in the analysis of multidimensional shock waves and related free boundary problems through several longstanding fundamental shock problems in continuum mechanics. The solution of these free boundary problems involves dealing with several core difficulties we have to face in the analysis of partial differential equations (PDEs). These include nonlinear PDEs of mixed hyperbolic-elliptic type, nonlinear degenerate elliptic PDEs, nonlinear degenerate hyperbolic PDEs, corner singularities (especially when free boundaries meet the fixed boundaries where the nonlinear PDEs experience their degeneracy), among others. These difficulties also arise in many further fundamental problems in continuum mechanics, differential geometry, mathematical physics, and other areas. Some further developments, open problems, and mathematical challenges in this direction are also addressed.Date: Friday, March 31, 2017