Existence, uniqueness and concentration for a system of PDEs involving the Laplace–Beltrami operator

Abstract

In this paper we derive a model for heat diffusion in a composi te medium in which the different components are separated by thermally active interf ac s. The previous result is obtained via a concentrated capacity procedure and leads to a non-sta ntard system of PDEs involving a Laplace-Beltrami operator acting on the interface. For suc h a system well-posedness is proved using contraction mapping and abstract parabolic problems theory. Finally, the exponential convergence (in time) of the solutions of our system to a steady s tate is proved. 2010 Mathematics Subject Classification: Primary 35K20; Secondary 35K90, 35B40.