Stability of non-classical thermoelasticity mixture problems

Margareth S. Alves; Rodrigo N. Monteiro

doi:10.3934/cpaa.2020216

Article Contents

2020, Volume 19, Issue 10: 4879-4898. Doi: 10.3934/cpaa.2020216

This issue Previous Article On the behavior of the free boundary for a one-phase Bernoulli problem with mixed boundary conditions Next Article Subsonic solutions to a shock diffraction problem by a convex cornered wedge for the pressure gradient system

Stability of non-classical thermoelasticity mixture problems

Margareth S. Alves^, and
Rodrigo N. Monteiro

Department of Mathematics, Federal University of Viçosa, Viçosa, MG, 36570-000, Brazil

^* Corresponding author
^* Corresponding author

Received: November 2019

Revised: May 2020

Published: July 2020

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Brasil (CAPES) - Finance Code 001, and by Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG).

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Abstract

We discuss the stability problem for binary mixtures systems coupled with heat equations. The present manuscript covers the non-classical thermoelastic theories of Coleman-Gurtin and Gurtin-Pipkin - both theories overcome the property of infinite propagation speed (Fourier's law property). We first state the well-posedness and our main result is related to long-time behavior. More precisely, we show, under suitable hypotheses on the physical parameters, that the corresponding solution is stabilized to zero with exponential or rational rates.

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Mathematics Subject Classification: 35L20, 35B40.

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