English

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