Almost global existence for quasilinear wave equations in waveguides with Neumann boundary conditions

Details Almost global existence for quasilinear wave equations in waveguides with Neumann boundary conditions Almost global existence for quasilinear wave equations in waveguides with Neumann boundary conditions

2005-09-14

arxiv.org/abs/math/0509326v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

In this paper, we prove almost global existence of solutions to certain quasilinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides with Neumann boundary conditions. We use a Galerkin method to expand the Laplacian of the compact base in terms of its eigenfunctions. For those terms corresponding to zero modes, we obtain decay using analogs of estimates of Klainerman and Sideris. For the nonzero modes, estimates for Klein-Gordon equations, which provide better decay, are available.

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