Inverse problems for a perturbed dissipative half-space.

*(English)*Zbl 0842.35135Authors’ abstract: “This paper addresses the scattering of acoustic and electromagnetic waves from a perturbed dissipative half-space. For simplicity, the perturbation is assumed to have compact support.

Section 1 discusses the application that motivated this work and explains how the scalar model used here is related to Maxwell’s equations. Section 2 introduces three formulations for direct and inverse problems for the half-space geometry. Two of these formulations relate to scattering problems, and the third to a boundary value problem. Section 3 shows how the scattering problems can be related to the boundary value problem. This shows that the three inverse problems are equivalent in a certain sense. In section 4, the boundary value problem is used to outline a simple way to formulate a multidimensional layer stripping procedure. This procedure is unstable and does not constitute a practical algorithm for solving the inverse problem.

The paper concludes with three appendices, the first two of which carry out a careful construction of solutions of the direct problems and the third of which contains a discussion of some properties of the scattering operator”.

Section 1 discusses the application that motivated this work and explains how the scalar model used here is related to Maxwell’s equations. Section 2 introduces three formulations for direct and inverse problems for the half-space geometry. Two of these formulations relate to scattering problems, and the third to a boundary value problem. Section 3 shows how the scattering problems can be related to the boundary value problem. This shows that the three inverse problems are equivalent in a certain sense. In section 4, the boundary value problem is used to outline a simple way to formulate a multidimensional layer stripping procedure. This procedure is unstable and does not constitute a practical algorithm for solving the inverse problem.

The paper concludes with three appendices, the first two of which carry out a careful construction of solutions of the direct problems and the third of which contains a discussion of some properties of the scattering operator”.

Reviewer: Dang Dinh Ang (Ho Chi Minh City)

##### MSC:

35R30 | Inverse problems for PDEs |

35Q60 | PDEs in connection with optics and electromagnetic theory |