Energy decay rate of a mixed type II and type III thermoelastic system

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November 2010, 14(4): 1433-1444. doi: 10.3934/dcdsb.2010.14.1433

Energy decay rate of a mixed type II and type III thermoelastic system

Zhuangyi Liu ^1, and Ramón Quintanilla ^2,

1.	Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812-2496
2.	Departament de Matemàtica Aplicada 2, ETSEIAT–UPC, C. Colom 11, 08222 Terrassa, Barcelona

Received October 2009 Revised February 2010 Published August 2010

Abstract
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In this paper, we study the energy decay rate for a mixed type II and type III thermoelastic system. The system consists of a wave equation and a heat equation of type III in one part of the domain; a wave equation and a heat equation of type II in another part of the domain, coupled in certain pattern. When the damping coefficient function satisfies certain conditions at the interface, a polynomial type decay rate is obtained. This result is proved by verifying the frequency domain conditions.

Keywords: thermoelasticity, polynomial decay rate, frequency domain..

Mathematics Subject Classification: Primary: 35Q70, 35B40; Secondary: 74F0.

Citation: Zhuangyi Liu, Ramón Quintanilla. Energy decay rate of a mixed type II and type III thermoelastic system. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1433-1444. doi: 10.3934/dcdsb.2010.14.1433

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