Exponential decay to partially thermoelastic materials

Jaime E. Muñoz Rivera; Vanilde Bisognin; Eleni Bisognin

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 3, page 605-629
  • ISSN: 0392-4041

Abstract

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We study the thermoelastic system for material which are partially thermoelastic. That is, a material divided into two parts, one of them a good conductor of heat, so there exists a thermoelastic phenomenon. The other is a bad conductor of heat so there is not heat flux. We prove for such models that the solution decays exponentially as time goes to infinity. We also consider a nonlinear case.

How to cite

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Muñoz Rivera, Jaime E., Bisognin, Vanilde, and Bisognin, Eleni. "Exponential decay to partially thermoelastic materials." Bollettino dell'Unione Matematica Italiana 5-B.3 (2002): 605-629. <http://eudml.org/doc/195374>.

@article{MuñozRivera2002,
abstract = {We study the thermoelastic system for material which are partially thermoelastic. That is, a material divided into two parts, one of them a good conductor of heat, so there exists a thermoelastic phenomenon. The other is a bad conductor of heat so there is not heat flux. We prove for such models that the solution decays exponentially as time goes to infinity. We also consider a nonlinear case.},
author = {Muñoz Rivera, Jaime E., Bisognin, Vanilde, Bisognin, Eleni},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {605-629},
publisher = {Unione Matematica Italiana},
title = {Exponential decay to partially thermoelastic materials},
url = {http://eudml.org/doc/195374},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Muñoz Rivera, Jaime E.
AU - Bisognin, Vanilde
AU - Bisognin, Eleni
TI - Exponential decay to partially thermoelastic materials
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/10//
PB - Unione Matematica Italiana
VL - 5-B
IS - 3
SP - 605
EP - 629
AB - We study the thermoelastic system for material which are partially thermoelastic. That is, a material divided into two parts, one of them a good conductor of heat, so there exists a thermoelastic phenomenon. The other is a bad conductor of heat so there is not heat flux. We prove for such models that the solution decays exponentially as time goes to infinity. We also consider a nonlinear case.
LA - eng
UR - http://eudml.org/doc/195374
ER -

References

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  1. DAFERMOS, C. M., On the existence and the asymptotic stability of solution to the equation of linear thermoelasticity, Arch. Rat. Mech Anal., 29 (1968), 241-271. Zbl0183.37701MR233539
  2. GREENBERG, J. M.- TATSIEN, LI, The effect of the boundary damping for the quasilinear wave equation, Journal of Differential Equations, 52 (1) (1984), 66-75. Zbl0576.35080MR737964
  3. HRUSA, W. J.- MESSAOUDI, S. A., On formation of singularities in one dimensional nonlinear thermoelasticity, Arch. Rational Mech. Anal., 111 (1990), 135-151. Zbl0712.73023MR1057652
  4. KIM, J. U., On the energy decay of a linear thermoelastic bar and plate, SIAM J. Math. Anal., 23 (1992), 889-899. Zbl0755.73013MR1166563
  5. KOMORNIK, V., Rapid boundary stabilization of the wave equation, SIAM J. Control and Optimization, 29 (1991), 197-208. Zbl0749.35018MR1088227
  6. KOMORNIK, V.- ZUAZUA, ENRIKE, A direct method for the boundary stabilization of the wave equation, J. Math. pures et appl., 69 (1990), 33-54. Zbl0636.93064MR1054123
  7. LASIECKA, I., Global uniform decay rates for the solution to the wave equation with nonlinear boundary conditions, Applicable Analysis47 (1992), 191-212. Zbl0788.35008MR1333954
  8. MUÑOZ RIVERA, J. E., Energy decay rates in linear thermoelasticity, Funkcialaj Ekvacioj, 35 (1992), 19-30. Zbl0838.73006MR1172418
  9. MUÑOZ RIVERA, J. E.- OLIVERA, M. L., Stability in inhomogeneous and anisotropic thermoelasticity, Bollettino della Unione Matematica Italiana, (7) 11-A (1997), 115-127. Zbl0891.73012MR1438361
  10. NAKAO, M., Decay of solutions of the wave equation with a local degenerate dissipation, Israel J. Math., 95 (1996), 25-42. Zbl0860.35072MR1418287
  11. NAKAO, M., Decay of solutions of the wave equation with a local nonlinear dissipation, Math. Ann., 305, No. 3 (1996), 403-417. Zbl0856.35084MR1397430
  12. ONO, K., A stretched string equation with a boundary dissipation, Kyushu J. of Math., 28, No. 2 (1994), 265-281. Zbl0823.35166MR1294530
  13. RACKE, R., On the time asymptotic behaviour of solutions in thermoelasticity, Proceeding of the Royal Society of Edinburgh, 107A (1987), 289-298. Zbl0631.73007MR924522
  14. RACKE, R.- SHIBATA, Y., Global smooth solution and asymptotic stability in one dimensional nonlinear thermoelasticity, Arch. Rat. Mech. Anal., 116 (1991), 1-34. Zbl0756.73012MR1130241
  15. RACKE, R.- SHIBATA, Y.- ZHENG, S., Global solvability and exponential stability in one dimensional nonlinear thermoelasticity, Quarterly Appl. Math., 51, No. 4 (1993), 751-763. Zbl0804.35132MR1247439
  16. SHEN, WEIXI- ZHENG, SONGMU, Global smooth solution to the system of one dimensional Thermoelasticity with dissipation boundary condition, Chin. Ann. of Math., 7B (3) (1986), 303-317. Zbl0608.73013
  17. SLEMROD, M., Global existence, uniqueness and asymptotic stability of classical smooth solution in one dimensional non linear thermoelasticity, Arch. Rat Mech. Ana., 76 (1981), 97-133. Zbl0481.73009MR629700
  18. TEMAN, R., Infinite Dimensional Dynamical systems in Mechanics and Physics, Springer-VerlagNew York Inc. (1988). Zbl0662.35001
  19. ZHENG, S., Global solution and application to a class of quasi linear hyperbolic-parabolic coupled system, Sci. Sínica, Ser. A, 27 (1984), 1274-1286. Zbl0581.35056MR794293
  20. ZUAZUA, E., Uniform stabilization of the wave equation by nonlinear wave equation boundary feedback, SIAM J. control and optimization, 28 (1990), 466-477. Zbl0695.93090MR1040470
  21. ZUAZUA, E., Exponential decay for the semilinear wave equation with locally distribuited damping, Comm. P.D.E., 15 (1990), 205-235. Zbl0716.35010MR1032629

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