Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity
ESAIM: Control, Optimisation and Calculus of Variations, Tome 3 (1998), pp. 23-48. 
@article{COCV_1998__3__23_0,
     author = {Liu, Weijiu},
     title = {Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {23--48},
     publisher = {EDP-Sciences},
     volume = {3},
     year = {1998},
     mrnumber = {1610226},
     zbl = {0917.93032},
     language = {en},
     url = {http://www.numdam.org/item/COCV_1998__3__23_0/}
}
TY  - JOUR
AU  - Liu, Weijiu
TI  - Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 1998
SP  - 23
EP  - 48
VL  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/COCV_1998__3__23_0/
LA  - en
ID  - COCV_1998__3__23_0
ER  - 
%0 Journal Article
%A Liu, Weijiu
%T Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 1998
%P 23-48
%V 3
%I EDP-Sciences
%U http://www.numdam.org/item/COCV_1998__3__23_0/
%G en
%F COCV_1998__3__23_0
Liu, Weijiu. Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 3 (1998), pp. 23-48. http://www.numdam.org/item/COCV_1998__3__23_0/

[1] R. Adams: Sobolev spaces, Academic Press, New York, 1975. | MR | Zbl

[2] F. Alabau, V. Komornik: Boundary observability, controllability and stabilization of linear elastodynamic systems, SIAM J. Control Optim., to appear. | MR | Zbl

[3] G. Avalos, I. Lasiecka: Exponential stability of a free thermoelastic system without mechanical dissipation, SIAM J. Math. Anal., to appear. | MR | Zbl

[4] C. Bardos, G. Lebeau, J. Rauch: Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Control Optim. 30, 1992, 1024-1065. | MR | Zbl

[5] J.A. Burns, Z.Y. Liu, S. Zheng: On the energy decay of a linear thermoelastic bar, J. Math. Anal. Appl., 179, 1993, 574-591. | MR | Zbl

[6] E. Bisognin, V. Bisognin, G.P. Menzala, E. Zuazua: On exponential stability for the Von Kármán equations in the presence of thermal effects, Math. Methods Appl. Sci., to appear. | Zbl

[7] G. Chen: Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain, J. Math. Pures Appl., 58, 1979, 249-273. | MR | Zbl

[8] S. Chirita: On the asymptotic partition of the energy in linear thermoelasticity, Quart. Appl. Math., 45, 1987, 327-340. | MR | Zbl

[9] C.M. Dafermos: On the existence and the asymptotic stability of solution to the equations of linear thermoelasticity, Arch. Rational Mech. Anal., 29, 1968, 241-271. | MR | Zbl

[10] G. Dassios, M. Grillakis: Dissipation rates and partition of energy in thermoelasticity, Arch. Rational Mech. Anal., 87, 1984, 49-91. | MR | Zbl

[11] P. Grisvard: Contrôlabilité exacte des solutions de l'équation des ondes en présence de singularités, J. Math. Pures Appl., 68, 1989, 215-259. | MR | Zbl

[12] S.W. Hansen: Exponential energy decay in a linear thermoelastic rod, J. Math. Anal. Appl., 167, 1992, 429-442. | MR | Zbl

[13] S.W. Hansen: Boundary control of a one-dimensional linear thermoelastic rod, SIAM J. Control Optim., 32, 1994, 1054-1074. | MR | Zbl

[14] J.U. Kim: On the energy decay of a linear thermoelastic bar and plate, SIAM J. Math. Anal., 23, 1992, 889-899. | MR | Zbl

[15] V. Komornik: Exact controllability and stabilization: The multiplier method, John Wiley & Sons, Masson, Paris, 1994. | MR | Zbl

[16] V. Komornik, E. Zuazua: A direct method for the boundary stabilization of the wave equation, J. Math. Pures Appl., 69, 1990, 33-54. | MR | Zbl

[17] A.D. Kovalenko: Thermoelasticity, basic theory and applications, Wolters-Noordhoff Publishing, Groningen, Netherlands, 1969. | Zbl

[18] J. Lagnese: Decay of solutions of wave equations in a bounded region with boundary dissipation, J. Differential Equations, 50, 1983, 163-182. | MR | Zbl

[19] J. Lagnese: Boundary stabilization of linear elastodynamic systems, SIAM J. Control Optim., 21, 1983, 968-984. | MR | Zbl

[20] J. Lagnese: Boundary Stabilization of Thin Plates, in SIAM Studies in Applied Mathematics, 10, SIAM Publications, Philadelphia, 1989. | MR | Zbl

[21] J. Lagnese: The reachability problem for thermoelastic plates, Arch. Rational Mech. Anal., 112 ( 1990), 223-267. | MR | Zbl

[22] J. Lagnese, J-.L. Lions: Modelling analysis and control of thin plates, Masson, Paris, 1989. | MR | Zbl

[23] P. Lax, R.S. Phillips: Scattering theory, Revised Edition, Academic Press INC., Boston, 1989. | MR | Zbl

[24] G. Lebeau, L. Robbiano: Contrôle exact de l'équation de la chaleur, Comm. Partial Differential Equations, 20 (1 & 2), 1995, 335-356. | MR | Zbl

[25] G. Lebeau, E. Zuazua: Sur la décroissance non uniforme de l'énergie dans le système de la thermoélasticité linéaire, C. R. Acad. Sci. Paris Sér. I Math., 324, 1997409-415. | MR | Zbl

[26] G. Lebeau, E. Zuazua: Null controllability of a system of linear thermoelasticity, Arch. Rational Mech. Anal., to appear. | MR | Zbl

[27] G. Leugering: On boundary feedback stabilization of a viscoelastic membrance, Dynam. Stability Systems, 4, 1989, 71-79. | MR | Zbl

[28] G. Leugering: On boundary feedback stabilization of a viscoelastic beam, Proc. Roy. Soc. Edinburgh Sect. A, 114, 1990, 57-69. | MR | Zbl

[29] G. Leugering: A decomposition method for integro-partial differential equations and applications, J. Math. Pures Appl., 71, 1992, 561-587. | MR | Zbl

[30] J.-L. Lions: Controlabilité exacte perturbations et stabilisation de systèmes distribues, Tome 2, Perturbations, Masson, Paris, 1988. | MR | Zbl

[31] J.-L. Lions, E. Magenes: Non-homogeneous boundary value problems and applications, vol. I and II, Springer-Verlag, New York, 1972. | MR | Zbl

[32] J.-L. Lions, E. Zuazua, A generic Uniqueness Resuit for the Stokes system and its control theoretical consequences, in Partial Differential Equations and Applications, P. Marcellini, G.T. Talenti, E. Vesentini, Eds., Lecture Notes in Pure and Applied Mathematics, 177, 221-235, Marcel Dekker, Inc., New York, 1996. | MR | Zbl

[33] W.J. Liu, The exponential stabilization of the higher-dimensional linear thermoviscoelasticity, J. Math. Pures Appl., to appear. | Zbl

[34] Z. Liu, M. Renardy: A note on the equations of thermoelastic plates, Appl. Math. Letters, 8, 1995, 1-6. | MR | Zbl

[35] Z. Liu, S. Zheng: Exponential stability of the semigroup associated with a thermoelastic system, Quart. Appl. Math., LI, 1993, 535-545. | MR | Zbl

[36] Z. Liu, S. Zheng: Exponential stability of the Kirchoff plate with thermal or viscoelastic damping, Quart. Appl. Math, to appear. | MR | Zbl

[37] G.P. Menzala, E. Zuazua: Explicit exponential decay rates for solutions of von Kármán's system of thermoelastic plates, C. R. Acad. Sci. Paris Sér. I Math., 324, 1997, 49-54. | MR | Zbl

[38] G.P. Menzala, E. Zuazua: Energy decay rates for the Von Kármán system of thermoelastic plates, Adv. Differential Equations, to appear. | Zbl

[39] C.S. Morawetz: Exponential decay of solutions of the wave equation, Comm. Pure Appl. Math., 19, 1966, 439-444. | MR | Zbl

[40] K. Narukawa: Boundary value control of thermoelastic systems, Hiroshima Math. J., 13, 1983, 227-272. | MR | Zbl

[41] A. Pazy: Semigroup of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983. | MR | Zbl

[42] D.C. Pereira, G.P. Menzala: Exponential decay of solutions to a coupled system of equations of linear thermoelasticity, Comput. Appl. Math., 8, 1989, 193-204. | MR | Zbl

[43] J.E.M. Rivera: Decomposition of the displacement vector field and decay rates in linear thermoelasticity, SIAM J. Math. Anal. 24, 1993, 390-406. | MR | Zbl

[44] J.E.M. Rivera, R. Racke: Smoothing properties, decay and global existence of solutions to nonlinear coupled systems of thermoelastic type, SBF series No. 287, Bonn University, 1993.

[45] D.L. Russell: Exact boundary value controlability theorems for wave and heat processes in star-complemented regions, in Differential games and control theory, Roxin, Liu, and Sternberg, Eds., Marcel Dekker Inc., New York, 1974, 291-319. | MR | Zbl

[46] D.L. Russell: Decay rates for weakly damped systems in Hilbert space obtained with control-theoretic methods, J. Differential Equations, 19, 1975, 344-370. | MR | Zbl

[47] L. De Teresa, E. Zuazua: Controllability of the linear system of thermoelastic plates, Adv. Differential Equations, 1, 3, 1996, 369-402. | MR | Zbl

[48] E. Zuazua: Controllability of the linear system of thermoelasticity, J. Math. Pures. Appl., 74, 1995, 291-315. | MR | Zbl