@article{COCV_1999__4__419_0, author = {Martinez, Patrick}, title = {A new method to obtain decay rate estimates for dissipative systems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {419--444}, publisher = {EDP-Sciences}, volume = {4}, year = {1999}, mrnumber = {1693904}, zbl = {0923.35027}, language = {en}, url = {http://archive.numdam.org/item/COCV_1999__4__419_0/} }
TY - JOUR AU - Martinez, Patrick TI - A new method to obtain decay rate estimates for dissipative systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 1999 SP - 419 EP - 444 VL - 4 PB - EDP-Sciences UR - http://archive.numdam.org/item/COCV_1999__4__419_0/ LA - en ID - COCV_1999__4__419_0 ER -
Martinez, Patrick. A new method to obtain decay rate estimates for dissipative systems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 4 (1999), pp. 419-444. http://archive.numdam.org/item/COCV_1999__4__419_0/
[1] On a quasilinear wave equation with a strong damping. Funkcial. Ekvac. 41 ( 199867-78. | MR | Zbl
,[2] Analysis and control of nonlinear infinite dimensional systems. Academic Press, New York ( 1993). | MR | Zbl
,[3] Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary. SIAM J. Control Optim. 30 ( 1992) 1024-1065. | MR | Zbl
, and ,[4] Sharp estimates of the energy for the solutions of some dissipative second order evolution equations. Potential Anal. 1 ( 1992) 265-289. | MR | Zbl
,[5] Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain. J. Math. Pures Appl. 58 ( 1979) 249-274. | MR | Zbl
,[6] Asymptotic behavior of solutions of the one dimensional wave equation with a nonlinear boundary stabilizer. SIAM J. Control Optim. 27 ( 1989) 758-775. | MR | Zbl
and ,[7] Décroissance de l'énergie pour certaines équations hyperboliques semilinéaires dissipatives. Thèse de 3e cycle, Université Pierre et Marie Curie ( 1984).
,[8] Stabilization of second order evolution equations by unbounded nonlinear feedback in. Proc. of the Fifth IFAC Symposium on Control of Distributed Parameter Systems, Perpignan ( 1989) 101-116. | Zbl
, and ,[9] Decay of solutions of wave equations in a star-shaped domain with non-linear boundary feedback. Asymptotic Analysis 7 ( 1993) 159-177. | MR | Zbl
and ,[10] Asymptotic behavior of solutions of evolutions equationsNonlinear evolution equations, M.G. Crandall, Ed., Academic Press, New-York ( 1978) 103-123. | MR | Zbl
,[11] Comportement à l'infini pour une équation des ondes non linéaire dissipative. C. R. Acad. Sci. Paris Sér. A 287 ( 1978507-509. | Zbl
,[12] Oscillations forcées pour certains systèmes dissipatifs non linéaires. Publication du Laboratoire d'Analyse Numérique No. 78010, Université Pierre et Marie Curie, Paris ( 1978).
,[13] Decay estimates for some semilinear damped hyperbolic problems. Arch. Rat. Mech. Anal. 100 ( 1988) 191-206. | MR | Zbl
and ,[14] Global stabilization of a dynamic Von Karman plate with nonlinear boundary feedback. Appl. Math. Optim. 31 ( 1995) 57-84. | MR | Zbl
and ,[15] Nonlinear boundary stabilization of parallelly connected Kirchhoff plates. Dynamics and Control 6 ( 1996) 263-292. | MR | Zbl
and ,[16] A direct method for the boundary stabilization of the wave equation. J. Maths Pures Appl. 69 ( 1990) 33-54. | MR | Zbl
and ,[17] On the nonlinear boundary stabilization of the wave equation. Chinese Ann. Math. Ser. B. 14 ( 1993153-164. | MR | Zbl
,[18] Exact Controllability and Stabilization RAM: Research in Applied Mathematics. Masson, Paris; John Wiley, Ltd., Chichester ( 1994). | MR | Zbl
,[19] On the decay of solutions of some semilinear hyperbolic problems. Panamer. Math. J. 6 ( 1996) 69-82. | MR | Zbl
,[20] Decay of solutions of wave equations in a bounded region with boundary dissipation. J. Differential Equations 50 ( 1983163-182. | Zbl
,[21] Boundary stabilization of thin plates. SIAM Studies in Appl. Math., Philadelphia, 1989. | MR | Zbl
,[22] Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping. J. Diff. Integr. Eq. 6 ( 1993) 507-533. | MR | Zbl
and ,[23] Uniform stabilizability of a full Von Karman System with nonlinear boundary feedback. SIAM J. Control Optim. 36 ( 1998) 1376-1422. | MR | Zbl
,[24] Boundary stabilization of a 3-dimensional structural acoustic model. J. Math. Pures Appl. 78 ( 1999203-232. | MR | Zbl
,[25] Contrôlabilité exacte et stabilisation de systèmes distribués, Vol. 1, Masson, Paris ( 1988). | MR | Zbl
,[26] Decay rates for dissipative wave equation, preprint. | MR
and ,[27] Decay of solutions of the wave equation with a local highly degenerate dissipationAsymptotic Analysis 19 ( 1999) 1-17. | MR | Zbl
,[28] A new method to obtain decay rate estimates for dissipative Systems with localized damping. Rev. Mat. Compl Madrid, to appear. | MR | Zbl
,[29] Asymptotic stability of the bounded or almost periodic solution of the wave equation with a nonlinear dissipative term. J. Math. Anal. Appl. 58 ( 1977) 336-343. | MR | Zbl
,[30] Decay of solutions of the wave equation with a local nonlinear dissipation. Math. Ann. 305 ( 1996) 403-417. | MR | Zbl
,[31] Stabilization of the wave equation with localized nonlinear damping. J. Differential Equations 145 ( 1998) 502-524. | MR | Zbl
,[32] Optimalité d'estimations d'énergie pour une équation des ondes amortie. C. R. Acad. Sci. Paris Sér. A, to appear. | Zbl
,[33] Optimality of energy estimates for a damped wave equation with polynomial or non polynomial feedbacks, submitted.
and ,[34] Stability and decay for a class of nonlinear hyperbolic problems. Asymptotic Analysis 1 ( 19881-28. | MR | Zbl
,[35] Uniform stabilization of the wave equation by nonlinear boundary feedback. SIAM J. Control and Optim. 28 ( 1990) 466-478. | MR | Zbl
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