Identification of Boundary Conditions in a Spherical Heat Conduction Transmission Problem

Abstract

Although numerous analytical and numerical methods have been developed for inverse heat conduction problems in single-layer materials, few methods address such problems in composite materials. The following paper studies inverse interface problems with unknown boundary conditions by using interior point observations for heat equations with spherical symmetry. The zero degeneracy at the left interval 0<r<R1 leads to solution difficulties in the one-dimensional interface problem. So, we first investigate the well-posedness of the direct (forward) problem in special weighted Sobolev spaces. Then, we formulate three groups of unknown boundary conditions and inverse problems upon internal point measurements for the heat equation with spherical symmetry. Second-order finite difference scheme approaches for direct and inverse problems are developed. Computational test examples illustrate the theoretical statements proposed.