Mathematics Colloquia and Seminars

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Mixed type PDEs


Speaker: John Hunter, UC Davis
Location: 693 Kerr
Start time: Thu, Oct 10 2002, 4:10PM

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.