The rate of convergence to the asymptotics for the wave equation in an exterior domain

TL;DR

This paper analyzes how solutions to the wave equation outside a non-trapping obstacle converge to the free wave solution over time, providing explicit convergence rates and insights into the radiation field via scattering data.

Contribution

It establishes the rate of convergence for the wave equation in exterior domains and links the radiation field to scattering data, advancing understanding of wave behavior in such settings.

Findings

Derived explicit convergence rates for wave solutions

Connected radiation fields to scattering data

Enhanced understanding of wave asymptotics in exterior domains

Abstract

In this paper we consider the mixed problem for the wave equation exterior to a non-trapping obstacle in odd space dimensions. We derive a rate of the convergence of the solution for the mixed problem to a solution for the Cauchy problem. As a by-product, we are able to find out the radiation field of solutions to the mixed problem in terms of the scattering data.