English

Uniform estimates for solutions of nonlinear focusing damped wave equations

Analysis of PDEs 2024-03-12 v1

Abstract

For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result applies in particular to the case of a cubic equation on a bounded domain of dimension 3.

Keywords

Cite

@article{arxiv.2403.06541,
  title  = {Uniform estimates for solutions of nonlinear focusing damped wave equations},
  author = {Thomas Perrin},
  journal= {arXiv preprint arXiv:2403.06541},
  year   = {2024}
}