Asymptotic Behaviour and Exponential Stability for a Thermoelastic Problem With Localized Damping

GAO Hong-jun; ZHAO Yu-juan

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GAO Hong-jun, ZHAO Yu-juan. Asymptotic Behaviour and Exponential Stability for a Thermoelastic Problem With Localized Damping[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1363-1372.

Citation:

GAO Hong-jun, ZHAO Yu-juan. Asymptotic Behaviour and Exponential Stability for a Thermoelastic Problem With Localized Damping[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1363-1372.

Citation:

GAO Hong-jun, ZHAO Yu-juan. Asymptotic Behaviour and Exponential Stability for a Thermoelastic Problem With Localized Damping[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1363-1372.

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Asymptotic Behaviour and Exponential Stability for a Thermoelastic Problem With Localized Damping

GAO Hong-jun¹,
ZHAO Yu-juan²

1.
Department of Mathematics, Nanjing Normal University, Nanjing 210097, P. R. China;

Received Date: 2005-06-28
Rev Recd Date: 2006-06-12
Publish Date: 2006-11-15

Abstract

Abstract

A semi-linear thermoelastic problem with localized damping is considered,which is one of the most important mathematical models in material science.The existence and decays exponentially to zero of solution of this problem were obtained.Moreover,the existence of absorbing sets was achieved in the non-homogeneous case.The result indicates that the system which we studied here is asymptotic stability.
- thermoelasticity,
- exponential decay,
- asymptotic behaviour,
- absorbing set

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References(10)

References

[1]	Hensen S W.Exponential energy decay in a linear thermoelastic rod[J].Journal of Mathematical Analysis and Application,1992,167(2):429—442. doi: 10.1016/0022-247X(92)90217-2
[2]	Komornik V.Rapid boundary stabilization of the wave equation[J].SIAM Journal on Control and Optimization,1991,l29(1):197—208.
[3]	Ono K.A stretched string equation with a boundary dissipation[J].Kyushu Journal of Mathematcs,1994,48(2):265—281. doi: 10.2206/kyushujm.48.265
[4]	Nakao M.Decay of solutions of the wave equation with a local nonlinear dissipation[J].Mathematiche Annalen,1996，305(3):403—417. doi: 10.1007/BF01444231
[5]	Nakao M.Decay of solutions of the wave equation with a local degenerate dissipation[J].Israel Journal of Mathematics,1996,95(1):25—42. doi: 10.1007/BF02761033
[6]	Zuazua E.Exponential decay for the semilinear wave equation with locally distributed damping[J].Communications in Partial Differential Equations,1990,15(2):205—235. doi: 10.1080/03605309908820684
[7]	Lions J- L.Contrhatoité Exacte, Perturbations et Stabilisation de Systèmes distribés[M].Tome 1.masson.Paris, 1998.
[8]	Bardos C,Lebeau G,Rauch J.Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary[J].SIAM Journal on Control and Optimization,1992,30(5):1024—1065. doi: 10.1137/0330055
[9]	Marzocchi A,Munoz Rivera J E，Naso M G.Asymptotic behaviour and exponential stability for a transmission problem in thermoelasticity[J].Math Methods Appl Sci,2002,25(11):955—980. doi: 10.1002/mma.323
[10]	Kim J U.On the energy decay of a linear thermoelastic bar and plate[J].SIAM Journal on Mathematical Analysis，1992，23(5):889—899. doi: 10.1137/0523047