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In this paper, we prove almost global existence of solutions to certainquasilinear wave equations with quadratic nonlinearities in infinitehomogeneous waveguides with Neumann boundary conditions. We use a Galerkinmethod to expand the Laplacian of the compact base in terms of itseigenfunctions. For those terms corresponding to zero modes, we obtain decayusing analogs of estimates of Klainerman and Sideris. For the nonzero modes,estimates for Klein-Gordon equations, which provide better decay, areavailable.

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