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

Metcalfe, Jason; Stewart, Ann

doi:10.1090/S0002-9947-07-04290-0

Almost global existence for quasilinear wave equations in waveguides with Neumann boundary conditions
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by Jason Metcalfe and Ann Stewart PDF

Trans. Amer. Math. Soc. 360 (2008), 171-188 Request permission

Abstract:

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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