An-Najah Staff

In this article we consider heat transfer in a non-convex system that consists of a union of finitely many opaque, conductive and bounded objects which have diffuse and grey surfaces and are surrounded by a perfectly transparent and non-conducting medium (such as vacuum). The resulting problem is non-linear and in general is non-coercive due to the non-locality of the boundary conditions. We discuss the solvability of the problem by proving the existence of a weak solution. We extend the analysis to address the parabolic case and to the case with non-linear material properties. Also we consider some cases when coercivity is obtained and state the corresponding stronger existence results.