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}
}