Center stable manifolds for the radial semi-linear wave equation outside a ball
Analysis of PDEs
2024-01-24 v1
Abstract
We consider the nonlinear wave equation, with a large exponent, power-like non-linearity, outside a ball of the Euclidean 3-dimensional space. In a previous article, we have proved that any global solution converges, up to a radiation term, to a stationary solution of the equation. In this work, we construct the center-stable manifold associated to each of the stationary solution, giving a complete description of the dynamics of global solutions. We also study the behavior of solutions close to each of the center-stable manifold.
Keywords
Cite
@article{arxiv.2401.12581,
title = {Center stable manifolds for the radial semi-linear wave equation outside a ball},
author = {Thomas Duyckaerts and Jianwei Urban Yang},
journal= {arXiv preprint arXiv:2401.12581},
year = {2024}
}