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

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dc.creatorMetcalfe, Jason
dc.creatorStewart, Ann
dc.date2005-09-14
dc.date.accessioned2026-07-07T05:23:12Z
dc.date.available2026-07-07T05:23:12Z
dc.descriptionIn 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.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0509326
dc.identifierhttp://arxiv.org/abs/math/0509326
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76343
dc.subjectAnalysis of PDEs
dc.subject35L70; 42B99
dc.titleAlmost global existence for quasilinear wave equations in waveguides with Neumann boundary conditions
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