TY - JOUR

T1 - Some characterizations of parallel hyperplanes in multi-layered heat conductors

AU - Sakaguchi, Shigeru

N1 - Funding Information:
This research was partially supported by the Grants-in-Aid for Scientific Research (B) (♯ 18H01126 and ♯ 17H02847 ) of Japan Society for the Promotion of Science .
Publisher Copyright:
© 2020 Elsevier Masson SAS

PY - 2020/8

Y1 - 2020/8

N2 - We consider the Cauchy problem for the heat diffusion equation in the whole space consisting of three layers with different constant conductivities, where initially the upper and middle layers have temperature 0 and the lower layer has temperature 1. Under some appropriate conditions, it is shown that, if either the interface between the lower layer and the middle layer is a stationary isothermic surface or there is a stationary isothermic surface in the middle layer near the lower layer, then the two interfaces must be parallel hyperplanes. Similar propositions hold true, either if a stationary isothermic surface is replaced by a surface with the constant flow property or if the Cauchy problem is replaced by an appropriate initial-boundary value problem.

AB - We consider the Cauchy problem for the heat diffusion equation in the whole space consisting of three layers with different constant conductivities, where initially the upper and middle layers have temperature 0 and the lower layer has temperature 1. Under some appropriate conditions, it is shown that, if either the interface between the lower layer and the middle layer is a stationary isothermic surface or there is a stationary isothermic surface in the middle layer near the lower layer, then the two interfaces must be parallel hyperplanes. Similar propositions hold true, either if a stationary isothermic surface is replaced by a surface with the constant flow property or if the Cauchy problem is replaced by an appropriate initial-boundary value problem.

KW - Constant flow property

KW - Heat diffusion equation

KW - Multi-layered heat conductors

KW - Stationary isothermic surface

UR - http://www.scopus.com/inward/record.url?scp=85087210828&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85087210828&partnerID=8YFLogxK

U2 - 10.1016/j.matpur.2020.06.007

DO - 10.1016/j.matpur.2020.06.007

M3 - Article

AN - SCOPUS:85087210828

VL - 140

SP - 185

EP - 210

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

SN - 0021-7824

ER -