AN INVERSE PROBLEM FOR A NONLINEAR WAVE EQUATION WITH DAMPING

Abstract

We consider an inverse problem of recovering two coefficients in a semi-linear wave equation. This equation contains a damping term and a term with a quadratic nonlinearity. The inverse problem consists in recovering coefficients under these terms as function of the space variable x ∈ R 3 . A forward problem for the equation with a point source is studied. As a result, the inverse problem reduce to two problems, one of them is the well known problem of X-ray tomography, the other one is the problem of the integral geometry with a with a special weight function. The latter problem is studied and a stability estimate for the solution of this problem is stated.