Polynomial decay to thermoelastic plates with memory
Author:
Pedro Gamboa Romero
Journal:
Quart. Appl. Math. 67 (2009), 553-558
MSC (2000):
Primary 35M10, 35B30
DOI:
https://doi.org/10.1090/S0033-569X-09-01136-8
Published electronically:
June 9, 2009
Previous version:
Original version posted May 6, 2009
Corrected version:
Current version corrects publisher's misspelling of "thermoelastic" in title.
MathSciNet review:
2547639
Full-text PDF Free Access
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Additional Information
Abstract: We consider the linear model of thermoelastic plates with memory and we show that the solution decays polynomially with rates that depend on the regularity of the initial data.
References
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References
- M. Fabrizio, B. Lazzari, J. E. Muñoz Rivera, Asymptotic behaviour of thermoelastic plates of weakly hyperbolic type, Differential Integral Equations 13 (2000) 1347-1370. MR 1787071 (2001h:74031)
- C. Giorgi, V. Pata, Stability of linear thermoelastic systems with memory, Math. Models Methods Appl. Sci 11 (2001) 627-644. MR 1832996 (2002e:74011)
- Maurizio Grasselli, J. E. Muñoz Rivera, V. Pata, On the energy decay of the linear thermoelastic plate with memory, J. Math. Anal. Appl. 309 (2005) 1-14. MR 2154022 (2006c:35281)
- M. E. Gurtin, A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Ration. Mech. Anal 31 (1968) 113-126. MR 1553521
- J. E. Muñoz Rivera, M. G. Naso, E. Vuk, Asymptotic behavior of the energy for electromagnetic systems with memory, Math. Methods. Appl. Sci. 7 (2004) 819-841. MR 2055321 (2005a:35268)
- J. E. Muñoz Rivera, R. Racke, Smoothing properties, decay and global existence of solutions to nonlinear coupled systems of thermoelastic type, SIAM J. Math. Anal. 26 (1995) 1547-1563. MR 1356459 (96h:35217)
- V. Pata, A. Zucchi, Attractors for a damped hyperbolic equation with linear memory, Adv. Math. Sci. Appl. 11 (2001) 505-529. MR 1907454 (2003f:35027)
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. MR 710486 (85g:47061)
- J. Pruss, On the spectrum of $C_0$-semigroups, Trans. Amer. Math. Soc. 284 (1984) 847-857. MR 743749 (85f:47044)
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Additional Information
Pedro Gamboa Romero
Affiliation:
Institute of Mathematics, Universidade Federal do Rio de Janeiro, Av. Brigadeiro Trompowski s/n, Caixa Postal 68530 CEP:21945-970.RJ., Brazil
Email:
pgamboa@im.ufrj.br
Keywords:
Thermoelastic plates,
polynomial decay,
materials with memory
Received by editor(s):
March 1, 2008
Published electronically:
June 9, 2009
Article copyright:
© Copyright 2009
Brown University
The copyright for this article reverts to public domain 28 years after publication.
