##### Department of Mathematics,

University of California San Diego

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### Math 248 - Analysis

## Christopher Sogge

#### Johns Hopkins University

## Nonlinear wave equations in waveguides

##### Abstract:

In joint work with J. Metcalfe and A. Stewart, we prove global and almost global existence theorems for nonlinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides. We can handle both the case of Dirichlet boundary conditions and Neumann boundary conditions. In the case of Neumann boundary conditions we need to assume a natural nonlinear Neumann condition on the quasilinear terms. The results that we obtain are sharp in terms of the assumptions on the dimensions for the global existence results and in terms of the lifespan for the almost global results. For nonlinear wave equations, in the case where the infinite part of wave guide has spatial dimension three, the hypotheses in the theorem concern whether or not the Laplacian for the compact base of the wave guide has a zero mode or not.

Host: Kate Okikiolu and Hans Lindblad

### May 18, 2004

### 10:30 AM

### AP&M 6218

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