A Coefficient Inverse Problem for a Diffusion–Relaxation Model on Disjoint Domains

Many important physical phenomena can be described by parabolic interface problems. An example is provided by a two-layer magnetic system symmetrically distributed over two disconnected domains. In this work, we consider an inverse problem for identifying a space-dependent diffusion coefficient in a parabolic equation defined on disjoint domains, based on final-time measurements. First, we discuss the well-posedness of the corresponding direct problem. Then, we develop an iterative method for solving the inverse problem, which is reformulated as a sequence of direct problems. A numerical implementation based on the finite difference method is presented, and results from numerical test examples are discussed.