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Mixed type PDEs
Optimization| Speaker: | John Hunter, UC Davis |
| Location: | 693 Kerr |
| Start time: | Thu, Oct 10 2002, 4:10PM |
Description
PDEs of mixed hyperbolic/elliptic type arise, among
other other areas, in transonic fluid flow and in
multi-dimensional Riemann problems for hyperbolic
conservation laws. The mathematical theory of mixed
type PDEs originated in 1923 with the remarkable
paper of Tricomi, which established the existence
of a solution of the (linear) Tricomi problem by
reducing it to a singular integral equation.
Nonlinear mixed type conservation laws, such as the equations for transonic flow, remain poorly
understood because of the combined difficulties
introduced by shocks and change of type. We will
describe some of the basic theory of linear mixed
type PDEs and some recent advances in understanding nonlinear mixed type PDEs.