Large time behavior of temperature in two-phase heat conductors

초록

We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities. The large time behavior of temperature, the solution of the problem, is studied when initially temperature is assigned to be 0 on one medium and 1 on the other. We show that under a certain geometric condition of the configuration of the media, temperature is stabilized to a constant as time tends to infinity. We also show by examples that temperature in general oscillates and is not stabilized. (c) 2021 Elsevier Inc. All rights reserved. MSC: primary 35K05; secondary 35K10, 35K15, 35B40, 35C06

키워드