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

Zhuangyi Liu; Ramón Quintanilla

doi:10.3934/dcdsb.2010.14.1433

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2010, Volume 14, Issue 4: 1433-1444. Doi: 10.3934/dcdsb.2010.14.1433

This issue Previous Article Global exact boundary controllability for first order quasilinear hyperbolic systems Next Article Second-order necessary/sufficient conditions for optimal control problems in the absence of linear structure

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: September 30, 2009

Revised: January 31, 2010

Published: May 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q70, 35B40; Secondary: 74F05.

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