Applied Math Seminar

Special Seminar
Friday, April 13, 2001
2:00 p.m.
Bldg 380, Room 383-N

A.S. Fokas
Imperial College

Differential Forms, Spectral Theory
and Boundary Value Problems

Abstract:

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

1. 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}.

2. Given a convex domain D\subset R^n, perform the spectral analysis of W.

3. Given appropriate boundary conditions, analyze the global relation \int_{\partial D} W=0.

For linear PDE's, relations of this method with the Ehrenpreis-Palamodov Principle, as well as relations with applied techniques such as the Wiener-Hopf Technique will be discussed.

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