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2013 Decay Property for Solutions in the Three-Phase-Lag Heat Conduction
Leila Djouamai , Belkacem Said-Houari
Commun. Math. Anal. 15(1): 99-114 (2013).
Abstract

In this paper, we consider the Cauchy problem of two models of the theory of heat conduction with three-phase-lag. Under appropriate assumptions on the material parameters, we show the optimal decay rate of the $L^2$norm of solutions. More precisely, we prove that in each model the $L^2$norm of the solution is decaying with the rate $(1+t)^{1/4}$ for initial data in $L^1(\mathbb{R})$. This decay rate is similar to the one of the heat kernel. Some faster decay rates have been also given for some weighted initial data in $L^1(\mathbb{R})$.

Copyright © 2013 Mathematical Research Publishers
Leila Djouamai and Belkacem Said-Houari "Decay Property for Solutions in the Three-Phase-Lag Heat Conduction," Communications in Mathematical Analysis 15(1), 99-114, (2013). https://doi.org/
Published: 2013
Vol.15 • No. 1 • 2013
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