Asymptotic behavior for a heat conduction problem with perfect-contact boundary condition

Abstract

In this paper we consider the heat conduction problem for a slab represented by the interval [0, 1]. The initial temperature is a positive constant, the flux at the left end is also a positive constant, and at the right end there is a perfect contact condition: u_x(1, t) + γu_t(1, t) = 0. We analyze the asymptotic behavior of these problems as γ approaches infinity, and present some numerical calculations.