Existence and blow up of small-amplitude nonlinear waves with a sign-changing potential
Analysis of PDEs
2007-05-23 v1
Abstract
We study the nonlinear wave equation with a sign-changing potential in any space dimension. If the potential is small and rapidly decaying, then the existence of small-amplitude solutions is driven by the nonlinear term. If the potential induces growth in the linearized problem, however, solutions that start out small may blow-up in finite time.
Keywords
Cite
@article{arxiv.math/0503171,
title = {Existence and blow up of small-amplitude nonlinear waves with a sign-changing potential},
author = {Paschalis Karageorgis},
journal= {arXiv preprint arXiv:math/0503171},
year = {2007}
}
Comments
34 pages, 1 figure