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<p>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 with each of the stationary solutions, giving a complete description of the dynamics of global solutions. We also study the behaviour of solutions close to each of the center-stable manifolds.</p>

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Center Stable Manifolds for the Radial Semi-linear Wave Equation Outside a Ball

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Thomas Duyckaerts,
  • Jianwei Urbain Yang

摘要

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 with each of the stationary solutions, giving a complete description of the dynamics of global solutions. We also study the behaviour of solutions close to each of the center-stable manifolds.