On the Energy Decay of a Linear Thermoelastic Bar and Plate

Abstract

Previous article Next article On the Energy Decay of a Linear Thermoelastic Bar and PlateJong Uhn KimJong Uhn Kimhttps://doi.org/10.1137/0523047PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIt is shown that the energy of a thermoelastic bar and plate decays exponentially fast. The energy method, combined with a multiplier technique and compactness property, is used.[1] Constantine Dafermos, On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity, Arch. Rational Mech. Anal., 29 (1968), 241–271 38:1860 0183.37701 CrossrefISIGoogle Scholar[2] William Day, Heat conduction within linear thermoelasticity, Springer Tracts in Natural Philosophy, Vol. 30, Springer-Verlag, New York, 1985viii+83 87c:73001 0577.73009 CrossrefGoogle Scholar[3] Scott Hansen, Exponential energy decay in a linear thermoelastic rod, J. Math. Anal. Appl., 167 (1992), 429–442 10.1016/0022-247X(92)90217-2 93f:35229 0755.73012 CrossrefISIGoogle Scholar[4] William Hrusa and , Michael A. Tarabek, On smooth solutions of the Cauchy problem in one-dimensional nonlinear thermoelasticity, Quart. Appl. Math., 47 (1989), 631–644 90m:35172 0692.73005 CrossrefISIGoogle Scholar[5] Song Jiang, Global existence of smooth solutions in one-dimensional nonlinear thermoelasticity, Proc. Roy. Soc. Edinburgh Sect. A, 115 (1990), 257–274 91i:35194 0723.35044 CrossrefISIGoogle Scholar[6] John Lagnese, Boundary stabilization of thin plates, SIAM Studies in Applied Mathematics, Vol. 10, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1989viii+176 91k:73001 0696.73034 LinkGoogle Scholar[7] J. L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. 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Anal., 76 (1981), 97–133 10.1007/BF00251248 83c:73056 0481.73009 CrossrefISIGoogle ScholarKeywordsenergy decaythermoelastic barthermoelastic plate Previous article Next article FiguresRelatedReferencesCited byDetails Global existence and blow-up for a thermoelastic system with p -Laplacian24 June 2021 | Applicable Analysis, Vol. 101, No. 18 Cross Ref Stabilization of non-homogeneous viscoelastic waves coupled with heat conduction due to Cattaneo-Vernotte6 July 2022 | Ricerche di Matematica, Vol. 27 Cross Ref Thermoelasticity with antidissipationDiscrete and Continuous Dynamical Systems - S, Vol. 15, No. 8 Cross Ref The MGT-Fourier model in the supercritical caseJournal of Differential Equations, Vol. 301 Cross Ref Can the Average Temperature Stabilize a System of Thermoelastic Plates?22 May 2021 | Vietnam Journal of Mathematics, Vol. 49, No. 3 Cross Ref Uniform Polynomial Decay and Approximation in Control of a Family of Abstract Thermoelastic Models28 August 2021 | Journal of 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