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

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 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.

Keywords

Wave equation / Center-stable manifold / Exterior problem / Blow-up / 35L05 / 35A01 / 35B40 / 35B44 / 37K40

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Funding

National Natural Science Foundation of China(12371239)

Labex MME-DII and the Institut Universitaire de France

RIGHTS & PERMISSIONS

Peking University