A remark on finding the coefficient of the dissipative boundary condition via the enclosure method in the time domain

TL;DR

This paper presents an analytical method to determine the dissipative boundary coefficient of an obstacle in a wave equation using the enclosure method, based on observed wave data from a single initial source.

Contribution

It introduces an explicit formula for computing the boundary coefficient at the nearest surface point, advancing inverse boundary problem techniques in the time domain.

Findings

Explicit formula for boundary coefficient computation

Applicable to wave equations with dissipative boundaries

Uses data from a single wave solution

Abstract

An inverse problem for the wave equation outside an obstacle with a {\it dissipative boundary condition} is considered. The observed data are given by a single solution of the wave equation generated by an initial data supported on an open ball. An explicit analytical formula for the computation of the coefficient at a point on the surface of the obstacle which is nearest to the center of the support of the initial data is given.