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VOL. 81 | 2019 Energy structure and asymptotic profile of the linearized system of thermo-elastic equation in lower space dimensions
Yuki Kimura, Takayoshi Ogawa

Editor(s) Keiichi Kato, Takayoshi Ogawa, Tohru Ozawa

Abstract

We consider the thermo-elastic problem in the homogeneous isentropic material. After introducing the Helmholtz free energy of the thermo-elastic body and deriving a first approximation of the motion of elastic body with thermal effect, we show an $L^p$-type dissipative-dispersive estimate of Nishihara-type for the linearized equations and it shows that the solution is asymptotically decomposed into solutions to a linear heat equation, a solution to a linear wave equation of exponentially decaying and a diffusive wave ([6]). Then the sharp asymptotic behavior of the solutions to linearized thermo-elastic equations is shown for the coupled elastic-thermal system. As a by-product, we also obtain the Nishihara-type $L^p$ decay estimate for damped wave equation as the limiting case.

Information

Published: 1 January 2019
First available in Project Euclid: 31 October 2019

zbMATH: 07176818

Digital Object Identifier: 10.2969/aspm/08110101

Subjects:
Primary: 35Q74, 74B15

Rights: Copyright © 2019 Mathematical Society of Japan

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