Asymptotic profile of solutions to the heat equation on thin plate with boundary heating

Abstract

Surface heating on thin plate is widely used in engineering processes, which is described by the heat equation on thin plate of thickness h>0 with Robin boundary condition on upper and lower faces of the plate. It is important for engineering to understand the solutions of the problem for small h>0. In this paper we obtain a sharp asymptotic profile of the solutions as the thickness h>0 approaches to zero.