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arXiv · 2401.12581

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

Thomas Duyckaerts·Jianwei Urban Yang
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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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Thomas Duyckaerts, Jianwei Urban Yang. 2024-01-23. Center stable manifolds for the radial semi-linear wave equation outside a ball. https://arxiv.org/abs/2401.12581

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