Uniqueness in Determination of a Straight Crack by the Two-Dimensional Wave Equation

Abstract

We consider an inverse problem of determining an unknown crack by the two-dimensional wave equation from boundary measurements. To this end, we deal with the initial-boundary value problem of the wave equation in a domain with a crack as a direct problem, and consider uniqueness of a solution to our inverse problem. We show unique solvability of the initial-boundary value problem in weighted Sobolev spaces, and show uniqueness in the inverse problem for a straight crack case.