On reconstruction of a cavity in a linearized viscoelastic body from infinitely many transient boundary data

Abstract

In this paper, a reconstruction problem of a cavity in a linearized viscoelastic body from dynamical boundary data is considered. As a result, we establish a formula extracting three kinds of information about the unknown cavity: the support function, the distance from an outer point of the body and the minimum radius of the open ball including the cavity centered at a point, with infinitely many sets of the boundary data. In the formula, observation time can be taken to be arbitrary.