AN INVERSE PROBLEM FOR THE WAVE EQUATION WITH NONLINEAR DUMPING

We study the inverse problem of recovering a coefficient at the nonlinearity in a second order hyperbolic equation with nonlinear damping. The unknown coefficient depends on one space variable x. Also, we consider the process of wave propagation along the semiaxis x > 0 given the derivative with respect to x at x = 0. As additional information in the inverse problem we consider the trace of a solution to the initial boundary value problem on a finite segment of the axis x = 0 and find the conditions for unique solvability of the direct problem. We also establish a local existence theorem and a global stability estimate for a solution to the inverse problem.