Uniform boundary stabilization of a thermoelastic bar with a nonlinear weak damping

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1. [1] Aassila M., Nouvelle approche à la stabilisation forte des systèmes distribués, C. R. Acad. Sci. Paris 324 (1997), 43-48. 
2. [2] Aassila M. , Strong asymptotic stability for n-dimensional thermoelasticity systems, Colloq. Math. 77 (1998), 133-139. Zbl0958.35012
3. [3] Ammar Khodja F., Benabdallah A. et Teniou D., Stabilisation d'un système similaire à celui de la thermoélasticité, C. R. Acad. Sci. Paris 322 (1996), 551-556. Zbl0847.35015
4. [4] Burns J., Liu Z. and Zheng S., On the energy decay of a thermoelastic bar, J. Anal. Math. Appl. 179 (1993), 574-591. Zbl0803.35150
5. [5] Dafermos C. M., On the existence and the asymptotic stability of solution to the equations of linear thermoelasticity, Arch. Rational Mech. Anal. 29 (1968), 241-271. Zbl0183.37701
6. [6] Gibson J. S., Rosen I. G. and Tao G., Approximation in control of thermolastic systems, SIAM J. Control Optim. 30 (1992), 1163-1189. Zbl0762.93051
7. [7] Hansen S. W., Exponential energy decay in a linear thermoelastic rod, J. Math. Anal. Appl. 167 (1992), 429-442. Zbl0755.73012
8. [8] Huang F. L., Characteristic condition for exponential stability of linear dynamical systems in Hilbert spaces, Ann. Differential Equations 1 (1985), 43-48. 
9. [9] Jiang S., Global existence of smooth solutions in one-dimensional nonlinear thermoelasticity, Proc. Roy. Soc. Edinburgh 115 (1990), 257-274. Zbl0723.35044
10. [10] Jiang S. , Global solution of the Neumann problem in one-dimensional nonlinear thermoelasticity, Nonlinear Anal. 19 (1992), 107-121. Zbl0770.73009
11. [11] Kim J. U., On the energy decay of a linear thermoelastic bar and plate, SIAM J. Math. Anal. 23 (1992), 889-899. Zbl0755.73013
12. [12] Komornik V., Exact Controllability and Stabilization, the Multiplier Method, Masson, Paris, 1994. Zbl0937.93003
13. [13] Komornik V. and Zuazua E., A direct method for the boundary stabilization of the wave equation, J. Math. Pures Appl. 69 (1990), 33-54. Zbl0636.93064
14. [14] Liu Z. Y. and Zheng S., Exponential stability of semi-group associated with thermoelastic system, Quart. Appl. Math. 51 (1993), 535-545. Zbl0803.35014
15. [15] Muñoz Rivera J. E., Energy decay rate in linear thermoelasticity, Funkcial. Ekvac. 35 (1992), 19-30. Zbl0838.73006
16. [16] Ponce G. and Racke R., Global existence of small solutions to the initial value problem for nonlinear thermoelasticity, J. Differential Equations 87 (1990), 70-83. Zbl0725.35065
17. [17] Racke R. and Shibata Y., Global smooth solutions and asymptotic stability in one-dimensional thermoelasticity, Arch. Rational Mech. Anal. 116 (1992), 1-34. Zbl0756.73012
18. [18] Shibata Y., Neumann problem for one-dimensional nonlinear thermoelasticity, in: Banach Center Publ. 27, Inst. Math., Polish Acad. Sci., 1990, 457-480. Zbl0802.35147
19. [19] Slemrod M., Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity, Arch. Rational Mech. Anal. 76 (1981), 97-133. Zbl0481.73009