American Institute of Mathematical Sciences

Advanced
August  2003, 3(3): 383-400. doi: 10.3934/dcdsb.2003.3.383

Stability in thermoelasticity of type III

Ramon Quintanilla 1, and  Reinhard Racke 2,

1. 

Department of Applied Mathematics II, UPC Terrassa, Colom 11, 08222 Terrassa, Spain
2. 

Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz

Received  October 2002 Revised  January 2003 Published  May 2003

We consider initial-boundary value problems in a hyperbolic thermoelastic system, called thermoelasticity of type III. First, we prove the exponential stability in one space dimension for different boundary conditions with energy methods and spectral methods, respectively. Then the exponential stability in more two or three space dimensions is proved for radially symmetric situations. Finally, the equipartition of energy is investigated.
Keywords: exponential stability, Hyperbolic thermoelasticity, radial symmetry., equipartition of energy.
Mathematics Subject Classification: 74F0.
Citation: 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
[1]

Gisèle Ruiz Goldstein, Jerome A. Goldstein, Fabiana Travessini De Cezaro. Equipartition of energy for nonautonomous wave equations. Discrete & Continuous Dynamical Systems - S, 2017, 10 (1) : 75-85. doi: 10.3934/dcdss.2017004
[2]

Marcello D'Abbicco, Giovanni Girardi, Giséle Ruiz Goldstein, Jerome A. Goldstein, Silvia Romanelli. Equipartition of energy for nonautonomous damped wave equations. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020364
[3]

Zhi-Ying Sun, Lan Huang, Xin-Guang Yang. Exponential stability and regularity of compressible viscous micropolar fluid with cylinder symmetry. Electronic Research Archive, 2020, 28 (2) : 861-878. doi: 10.3934/era.2020045
[4]

Monica Conti, Elsa M. Marchini, Vittorino Pata. Exponential stability for a class of linear hyperbolic equations with hereditary memory. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1555-1565. doi: 10.3934/dcdsb.2013.18.1555
[5]

Margareth S. Alves, Rodrigo N. Monteiro. Stability of non-classical thermoelasticity mixture problems. Communications on Pure & Applied Analysis, 2020, 19 (10) : 4879-4898. doi: 10.3934/cpaa.2020216
[6]

Orlando Lopes. Uniqueness and radial symmetry of minimizers for a nonlocal variational problem. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2265-2282. doi: 10.3934/cpaa.2019102
[7]

Ramon Quintanilla. Structural stability and continuous dependence of solutions of thermoelasticity of type III. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 463-470. doi: 10.3934/dcdsb.2001.1.463
[8]

Patricio Felmer, César Torres. Radial symmetry of ground states for a regional fractional Nonlinear Schrödinger Equation. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2395-2406. doi: 10.3934/cpaa.2014.13.2395
[9]

Wenxiong Chen, Congming Li. Radial symmetry of solutions for some integral systems of Wolff type. Discrete & Continuous Dynamical Systems - A, 2011, 30 (4) : 1083-1093. doi: 10.3934/dcds.2011.30.1083
[10]

Antonio Greco, Vincenzino Mascia. Non-local sublinear problems: Existence, comparison, and radial symmetry. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 503-519. doi: 10.3934/dcds.2019021
[11]

Sara Barile, Addolorata Salvatore. Radial solutions of semilinear elliptic equations with broken symmetry on unbounded domains. Conference Publications, 2013, 2013 (special) : 41-49. doi: 10.3934/proc.2013.2013.41
[12]

Dongbing Zha. Remarks on nonlinear elastic waves in the radial symmetry in 2-D. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 4051-4062. doi: 10.3934/dcds.2016.36.4051
[13]

Carlos E. Kenig, Frank Merle. Radial solutions to energy supercritical wave equations in odd dimensions. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1365-1381. doi: 10.3934/dcds.2011.31.1365
[14]

Soohyun Bae, Yūki Naito. Separation structure of radial solutions for semilinear elliptic equations with exponential nonlinearity. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4537-4554. doi: 10.3934/dcds.2018198
[15]

M. Grossi. Existence of radial solutions for an elliptic problem involving exponential nonlinearities. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 221-232. doi: 10.3934/dcds.2008.21.221
[16]

Nanhee Kim. Uniqueness and Hölder type stability of continuation for the linear thermoelasticity system with residual stress. Evolution Equations & Control Theory, 2013, 2 (4) : 679-693. doi: 10.3934/eect.2013.2.679
[17]

Gustavo Alberto Perla Menzala, Julian Moises Sejje Suárez. A thermo piezoelectric model: Exponential decay of the total energy. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5273-5292. doi: 10.3934/dcds.2013.33.5273
[18]

Hwai-Chiuan Wang. Stability and symmetry breaking of solutions of semilinear elliptic equations. Conference Publications, 2005, 2005 (Special) : 886-894. doi: 10.3934/proc.2005.2005.886
[19]

Luis Barreira, Claudia Valls. Delay equations and nonuniform exponential stability. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 219-223. doi: 10.3934/dcdss.2008.1.219
[20]

Xiaotao Huang, Lihe Wang. Radial symmetry results for Bessel potential integral equations in exterior domains and in annular domains. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1121-1134. doi: 10.3934/cpaa.2017054

2019 Impact Factor: 1.27

Tools

Metrics

  • PDF downloads (31)
  • HTML views (0)
  • Cited by (48)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences