American Institute of Mathematical Sciences

Advanced
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 & Continuous Dynamical Systems - B, 2010, 14 (4) : 1433-1444. doi: 10.3934/dcdsb.2010.14.1433
[1]

George Avalos, Roberto Triggiani. Rational decay rates for a PDE heat--structure interaction: A frequency domain approach. Evolution Equations & Control Theory, 2013, 2 (2) : 233-253. doi: 10.3934/eect.2013.2.233
[2]

Antonio Magaña, Alain Miranville, Ramón Quintanilla. On the time decay in phase–lag thermoelasticity with two temperatures. Electronic Research Archive, 2019, 27: 7-19. doi: 10.3934/era.2019007
[3]

Zhuangyi Liu, Ramón Quintanilla. Time decay in dual-phase-lag thermoelasticity: Critical case. Communications on Pure & Applied Analysis, 2018, 17 (1) : 177-190. doi: 10.3934/cpaa.2018011
[4]

Michiko Yuri. Polynomial decay of correlations for intermittent sofic systems. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 445-464. doi: 10.3934/dcds.2008.22.445
[5]

Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden. Minimum free energy in the frequency domain for a heat conductor with memory. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 793-816. doi: 10.3934/dcdsb.2010.14.793
[6]

Mohammed Aassila. On energy decay rate for linear damped systems. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 851-864. doi: 10.3934/dcds.2002.8.851
[7]

Bopeng Rao. Optimal energy decay rate in a damped Rayleigh beam. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 721-734. doi: 10.3934/dcds.1998.4.721
[8]

Denis Mercier, Virginie Régnier. Decay rate of the Timoshenko system with one boundary damping. Evolution Equations & Control Theory, 2019, 8 (2) : 423-445. doi: 10.3934/eect.2019021
[9]

Moez Daoulatli. Energy decay rates for solutions of the wave equation with linear damping in exterior domain. Evolution Equations & Control Theory, 2016, 5 (1) : 37-59. doi: 10.3934/eect.2016.5.37
[10]

George J. Bautista, Ademir F. Pazoto. Decay of solutions for a dissipative higher-order Boussinesq system on a periodic domain. Communications on Pure & Applied Analysis, 2020, 19 (2) : 747-769. doi: 10.3934/cpaa.2020035
[11]

Abdelaziz Soufyane, Belkacem Said-Houari. The effect of the wave speeds and the frictional damping terms on the decay rate of the Bresse system. Evolution Equations & Control Theory, 2014, 3 (4) : 713-738. doi: 10.3934/eect.2014.3.713
[12]

Yoshikazu Giga, Yukihiro Seki, Noriaki Umeda. On decay rate of quenching profile at space infinity for axisymmetric mean curvature flow. Discrete & Continuous Dynamical Systems - A, 2011, 29 (4) : 1463-1470. doi: 10.3934/dcds.2011.29.1463
[13]

Yongming Liu, Lei Yao. Global solution and decay rate for a reduced gravity two and a half layer model. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2613-2638. doi: 10.3934/dcdsb.2018267
[14]

Sergey Popov, Volker Reitmann. Frequency domain conditions for finite-dimensional projectors and determining observations for the set of amenable solutions. Discrete & Continuous Dynamical Systems - A, 2014, 34 (1) : 249-267. doi: 10.3934/dcds.2014.34.249
[15]

Ramon Quintanilla, Reinhard Racke. Stability in thermoelasticity of type III. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 383-400. doi: 10.3934/dcdsb.2003.3.383
[16]

Takeshi Taniguchi. The existence and decay estimates of the solutions to $3$D stochastic Navier-Stokes equations with additive noise in an exterior domain. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4323-4341. doi: 10.3934/dcds.2014.34.4323
[17]

Yaru Xie, Genqi Xu. The exponential decay rate of generic tree of 1-d wave equations with boundary feedback controls. Networks & Heterogeneous Media, 2016, 11 (3) : 527-543. doi: 10.3934/nhm.2016008
[18]

Marcelo M. Cavalcanti, Valéria N. Domingos Cavalcanti, Irena Lasiecka, Flávio A. Falcão Nascimento. Intrinsic decay rate estimates for the wave equation with competing viscoelastic and frictional dissipative effects. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 1987-2011. doi: 10.3934/dcdsb.2014.19.1987
[19]

Yong Zhou. Decay rate of higher order derivatives for solutions to the 2-D dissipative quasi-geostrophic flows. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 525-532. doi: 10.3934/dcds.2006.14.525
[20]

Maya Bassam, Denis Mercier, Ali Wehbe. Optimal energy decay rate of Rayleigh beam equation with only one boundary control force. Evolution Equations & Control Theory, 2015, 4 (1) : 21-38. doi: 10.3934/eect.2015.4.21

2018 Impact Factor: 1.008

Tools

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (12)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences