Large time behavior of temperature in two-phase heat conductors
Analysis of PDEs
2021-09-21 v2
Abstract
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 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.
Keywords
Cite
@article{arxiv.2102.02535,
title = {Large time behavior of temperature in two-phase heat conductors},
author = {Hyeonbae Kang and Shigeru Sakaguchi},
journal= {arXiv preprint arXiv:2102.02535},
year = {2021}
}
Comments
9 pages, to appear in Journal of Differential Equations