Scattering to a stationary solution for the superquintic radial wave equation outside an obstacle

TL;DR

This paper studies the superquintic radial wave equation outside a sphere, classifies stationary solutions, and shows that all global solutions asymptotically resemble a stationary solution plus radiation.

Contribution

It provides a complete classification of stationary solutions and proves asymptotic stability for all radial global solutions in this setting.

Findings

Classified all radial stationary solutions.

Proved asymptotic decomposition of solutions into stationary and radiation parts.

Established stability and long-term behavior of solutions.

Abstract

We consider the focusing wave equation outside a ball of $\R^3$, with Dirichlet boundary condition and a superquintic power nonlinearity. We classify all radial stationary solutions, and prove that all radial global solutions are asymptotically the sum of a stationary solution and a radiation term.