Nonlinear hyperbolic equations in infinite homogeneous waveguides

Details Nonlinear hyperbolic equations in infinite homogeneous waveguides Nonlinear hyperbolic equations in infinite homogeneous waveguides

2004-11-23

arxiv.org/abs/math/0411513v2

Mathematics

Analysis of PDEs

19 pages, To appear in Comm. PDE. Corrections were made to the KSS inequality for the Klein-Gordon equation (Prop. 2.3 and Lem

Scientific paper

In this paper we prove global and almost global existence theorems for nonlinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides. We can handle both the case of Dirichlet boundary conditions and Neumann boundary conditions. In the case of Neumann boundary conditions we need to assume a natural nonlinear Neumann condition on the quasilinear terms. The results that we obtain are sharp in terms of the assumptions on the dimensions for the global existence results and in terms of the lifespan for the almost global results. For nonlinear wave equations, in the case where the infinite part of the waveguide has spatial dimension three, the hypotheses in the theorem concern whether or not the Laplacian for the compact base of the waveguide has a zero mode or not.

Affiliated with

Also associated with

No associations

Rating

Nonlinear hyperbolic equations in infinite homogeneous waveguides does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nonlinear hyperbolic equations in infinite homogeneous waveguides, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonlinear hyperbolic equations in infinite homogeneous waveguides will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-599419