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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

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 and Continuous Dynamical Systems - B, 2010, 14 (4) : 1433-1444. doi: 10.3934/dcdsb.2010.14.1433
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