Analysis Seminar

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A Weak Dirichlet Problem for the Cold Plasma Model

Speaker: Thomas H. Otway, Yeshiva University

Location: Warren Weaver Hall 1302

Date: Thursday, February 20, 2014, 11 a.m.

Synopsis:

The open Dirichlet problem for elliptic-hyperbolic equations, in which data are prescribed on a proper subset of the boundary, has been studied for decades and arises, for example, in nozzle flow. But the closed Dirichlet problem for such equations, in which data are prescribed on the entire boundary, is not well known although it also arises naturally, e.g., in transonic flow about a profile and in plasma physics. Recently, Lupo, Morawetz, and Payne showed the existence of weak solutions to a closed Dirichlet problem for a class of equations having strong regularity in comparison to other elliptic-hyperbolic equations. We consider the same problem for an elliptic-hyperbolic equation, introduced by Weitzner in 1984, for which regularity is more problematic.