  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.
