Center stable manifolds for the radial semi-linear wave equation outside a ball

2024/01/23 by Duyckaerts, Thomas, Yang, Jianwei Urban
#35A01 #35B40 #35B44 #35L05 #37K40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.12581

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.

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