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# A. S. Fokas : Differential Forms, Spectral Theory and Boundary Value Problems

A new method will be reviewed for analyzing boundary value problems for linear and integrable nonlinear PDEs. This method involves the following:

- Given a PDE for
*q(x)*,*x*in**R**^{n}, construct a closed*(n-1)*-differential form*W(x,k)*,*k*in**C**^{n-1}. - Given a convex domain
*D*contained in**R**^{n}, perform the spectral analysis of*W* - Given appropriate boundary conditions, analyze the global relation

For linear PDEs, the relation of this method with the Ehrenpreis-Palamodov principle, as well as the relations with applied techniques such as the Weiner-Hopf technique will be discussed.

**Category**: Other Meetings and Events**Duration**: 58:20**Date**: April 4, 2001 at 4:00 PM**Views**: 21-
**Tags:**seminar, Department of Mathematics Seminar

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