Asymptotic stability and global existence in thermoelasticity with symmetry

Quarterly of Applied Mathematics

Volumn 56, Issue 2, 1998, Pages 259-275

  Jiang, S ^a,b   Munoz Rivera J E ^c   Racke, R ^d  

^a UNIVERSITY OF BONN   (Germany)

^b INSTITUTE OF APPLIED PHYSICS AND COMPUTATIONAL MATHEMATICS   (China)

^c FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^d UNIVERSITY OF KONSTANZ   (Germany)

Author keywords

Exponential decay; Global existence; Radial symmetry; Two and three dimensional thermoelasticity

Indexed keywords

ASYMPTOTIC STABILITY; PROBLEM SOLVING; SET THEORY; THEOREM PROVING; THERMOELASTICITY;

EXPONENTIAL DECAY; ISOTROPIC THERMOELASTICITY;

NONLINEAR EQUATIONS;

EID: 0032099611     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/1622566     Document Type: Article

References (25)

1. R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975
2. J. A. Burns, Z. Liu, and S. Zheng, On the energy decay of a linear thermoelastic bar, J. Math. Anal. Appl. 179, 574-591 (1993)
3. D. E. Carlson, Linear thermoelasticity, Handbuch der Physik VIa/2, Springer-Verlag, Berlin, 1972, pp. 297-346
4. D. Carvalho Pereira and G. Perla Menzala, Exponential decay of solutions to a coupled system of equations of linear thermoelasticity, Mat. Applic. Comp. 8, 193-240 (1989)
5. D. Carvalho Pereira and G. Perla Menzala, Exponential stability in linear thermoelasticity: the inhomogeneous case, Applic. Anal. 44, 21-36 (1992)
6. A. Chrzȩszczyk, Some existence results in dynamical thermoelasticity, Part I. Nonlinear case. Arch. Mech. 39, 605-617 (1987)
7. C. M. Dafermos, On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity, Arch. Rat. Mech. Anal. 29, 241-271 (1968)
8. S. W. Hansen, Exponential energy decay in a linear thermoelastic rod, J. Math. Anal. Appl. 167, 429-442 (1992)
9. D. B. Henry, Topics in Analysis, Publ. Secc. Mat., Univ. Autón. Barc. 31, 29-84 (1987)
10. D. B. Henry, A. Perissinitto Jr., and O. Lopes, On the essential spectrum of a semigroup of thermoelasticity, Nonlinear Anal. 21, 65-75 (1993)
11. S. Jiang, Global solutions of the Neumann problem in one-dimensional nonlinear thermoelasticity, Nonlinear Anal. 19, 107-121 (1992)
12. S. Jiang, Exponential decay and global existence of spherically symmetric solutions in thermoelasticity, SFB 256 Preprint, No. 351, Univ. Bonn, 1994
13. J. U. Kim, On the energy decay of a linear thermoelastic bar and plate, SIAM J. Math. Anal. 23, 889-899 (1992)
14. I. Lasiecka, J.-L. Lions, and R. Triggiani, Non homogeneous boundary value problems for second order hyperbolic operators, J. Math. Pures et Appl. 65, 149-192 (1986)
15. R. Leis, Initial boundary value problems in mathematical physics, B. G. Teubner Verlag, Stuttgart, John Wiley and Sons, Chichester, 1986
16. Z. Liu and S. Zheng, Exponential stability of semigroup associated with thermoelastic system, Quart. Appl. Math. 51, 535-545 (1993)
17. J. E. Muñoz Rivera, Energy decay rates in linear thermoelasticity, Funkcial. Ekvac. 35, 19-30 (1992)
18. J. E. Muñoz Rivera, Asymptotic behavior of the energy in thermo-visco-elasticity, Mat. Applic. Comp. 11, 45-71 (1992)
19. J. Ponce and R. Racke, Global existence of small solutions to the initial value problem for nonlinear thermoelasticity, J. Diff. Equations 87, 70-83 (1990)
20. R. Racke, On the time-asymptotic behaviour of solutions in thermoelasticity, Proc. Roy. Soc. Edinburgh 107A, 289-298 (1987)
21. R. Racke, On the Cauchy problem in nonlinear 3-d-thermoelasticity, Math. Z. 203, 649-682 (1990)
22. R. Racke, Blow-up in nonlinear three-dimensional thermoelasticity, Math. Meth. Appl. Sci. 12, 267-273 (1990)
23. R. Racke, Lectures on Nonlinear Evolution Equations, Aspects of Math., Vol. 19, Vieweg-Verlag, Braunschweig, 1992.
24. R. Racke, Exponential decay for a class of initial boundary value problems in thermoelasticity, Mat. Applic. Comp. 12, 67-80 (1993)
25. M. Slemrod, Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity, Arch. Rat. Mech. Anal. 76, 97-133 (1981)