Inverse Scattering for the Stationary Wave Equation with a Friction Term in Two Dimensions

Abstract

We consider the inverse scattering problem for the two dimensional stationary wave equation with a friction term. We prove that the friction coefficient is uniquely reconstructed from the scattering amplitude at a fixed low energy. A reconstruction procedure to identify the friction coefficient is also given. The method for the inverse scattering problem is based on the reduction argument reducing it to that of the inverse boundary value problem. We use the $\overline{\partial }$-method for a $3\times 3$ first order elliptic system to give the reconstruction procedure.