Uniqueness and numerical reconstruction for inverse problems dealing with interval size search

Abstract

<p style='text-indent:20px;'>We consider a heat equation and a wave equation in one spatial dimension. This article deals with the inverse problem of determining the size of the spatial interval from some extra boundary information on the solution. Under several different circumstances, we prove uniqueness, non-uniqueness and some size estimates. Moreover, we numerically solve the inverse problems and compute accurate approximations of the size. This is illustrated with several satisfactory numerical experiments.</p>