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

Stability in thermoelasticity of type III

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.
Citation: Ramon Quintanilla, Reinhard Racke. Stability in thermoelasticity of type III. Discrete and 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 and Continuous Dynamical Systems - S, 2017, 10 (1) : 75-85. doi: 10.3934/dcdss.2017004

[2]

Gervy Marie Angeles, Gilbert Peralta. Energy method for exponential stability of coupled one-dimensional hyperbolic PDE-ODE systems. Evolution Equations and Control Theory, 2022, 11 (1) : 199-224. doi: 10.3934/eect.2020108

[3]

Marcello D'Abbicco, Giovanni Girardi, Giséle Ruiz Goldstein, Jerome A. Goldstein, Silvia Romanelli. Equipartition of energy for nonautonomous damped wave equations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (2) : 597-613. doi: 10.3934/dcdss.2020364

[4]

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

[5]

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

[6]

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

[7]

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

[8]

Zhenjie Li, Chunqin Zhou. Radial symmetry of nonnegative solutions for nonlinear integral systems. Communications on Pure and Applied Analysis, 2022, 21 (3) : 837-844. doi: 10.3934/cpaa.2021201

[9]

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

[10]

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

[11]

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

[12]

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

[13]

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

[14]

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

[15]

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

[16]

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

[17]

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

[18]

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

[19]

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

[20]

Monica Conti, Lorenzo Liverani, Vittorino Pata. Thermoelasticity with antidissipation. Discrete and Continuous Dynamical Systems - S, 2022, 15 (8) : 2173-2188. doi: 10.3934/dcdss.2022040

2021 Impact Factor: 1.497

Metrics

  • PDF downloads (142)
  • HTML views (0)
  • Cited by (50)

Other articles
by authors

[Back to Top]