Nonlinear Boundary Feedback Stabilization for a Semilinear Kirchhoff Plate with Dissipation Acting only via Moments-Limiting Behavior

Journal of Mathematical Analysis and Applications

Volumn 229, Issue 2, 1999, Pages 452-479

  Ji, Guangcao ^a   Lasiecka, Irena ^b  

^a TEXAS TECH UNIVERSITY   (United States)

^b University of Virginia   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011521344     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.6170     Document Type: Article

References (28)

1. V. Barbu, "Nonlinear Semigroups and Differential Equations in Banach Spaces," Noordhoff, Groningen, 1976.
2. V. Barbu, "Analysis and Control of Nonlinear Infinite Dimensional Systems," Academic Press, New York, 1993.
3. A. Favini, M. A. Horn, I. Lasiecka, and D. Tataru, Global existence, uniqueness and regularity of solutions to a von Kármán system with nonlinear boundary dissipation, Differential Integral Equations 9 (1996), 267-294.
4. M. A. Horn, Exact controllability of the Euler-Bernoulli plate via bending moments only on the space of optimal regularity, J. Math. Anal. Appl. 167 (1992), 557-581.
5. M. A. Horn and I. Lasiecka, Asymptotic behavior with respect to thickness of boundary stabilizing feedback for the Kirchhoff plate, J. Differential Equations 114 (1994), 396-433.
6. M. A. Horn and I. Lasiecka, Global stabilization of a dynamic von Kármán plate with nonlinear boundary feedback, Appl. Math. Optim. 31 (1995), 57-84.
7. M. A. Horn and I. Lasiecka, Uniform decay of weak solutions to a von Kármán plate with nonlinear boundary dissipation, Differential Integral Equations 7 (1994), 885-908.
8. G. Ji, Uniform decay rates and asymptotic analysis of the von Kármán plate with nonlinear dissipation in boundary moments, Nonlinear Analysis, to appear.
9. 2 for semi-linear plates with nonlinear boundary dissipation acting via moments only, in "Proceedings of the IFIP Conference on Control of PDE's, Gainesville, March 1997" (W. Hager and P. Pardalos, Eds.), Optimal Control Theory, Algorithms and Applications, Vol. 15, pp. 224-246, Kluwer Academic, Dordrecht/Norwell, MA, 1998.
10. V. Komornik, "Exact Controllability and Stabilization, The Multiplier Method," Masson, Paris, 1994.
11. J. E. Lagnese, "Boundary Stabilization of Thin Plates," SIAM, Philadelphia, PA, 1989.
12. I. Lasiecka, Existence and uniqueness of the solutions to second order abstract equations with nonlinear and non-monotone boundary conditions, J. Nonlinear Anal. Methods, Appl. 23 (1994), 797-823.
13. I. Lasiecka, Exponential decay rates for the solutions of Euler-Bernoulli equations with boundary dissipation occurring in the moments only, J. Differential Equations 95 (1992), 169-182.
14. G. Lebeau, Contrôle de l'équations de Shrödinger, J. Math. Pures Appl. 71 (1992), 267-291.
15. J. L. Lions, "Optimal Control of Systems Governed by Partial Differential Equations," Spring-Verlag, Berlin/New York, 1971.
16. J. L. Lions, "Contrôlabité Exacte et Stabilization de Systèms Distribués," Vols. I and II, Masson, Paris, 1988.
17. W. Littman and S. Taylor, Smoothing evolution equations and boundary control theory, J. Analyse Math. 59 (1992), 117-131.
18. W. Littman, Boundary control theory for hyperbolic and parabolic partial differential equations, Ann. Scuola Norm. Sup. Pisa Ser IV 5 (1978), 567-580.
19. W. Littman, "The Role of Smoothing in Boundary Control," LNPAM Vol. 165, (G. Da Prato and L. Tubaro, Eds.), Lecture Notes in Pure and Applied Mathematics, pp. 137-143, Dekker, New York, 1994.
20. J. E. Lagnese and J. L. Lions, "Modeling Analysis and Control of Thin Plates," Masson, Paris, 1988.
21. J. L. Lions and E. Magenes, "Non-Homogeneous Boundary Value Problems and Applications," Springer-Verlag, Berlin/New York, 1972.
22. I. Lasiecka and D. Tataru, Uniform boundary stabilization of semi-linear wave equations with nonlinear boundary damping, Differential Integral Equations 6 (1993), 507-533.
23. Σ and homogeneous boundary displacement, J. Differential Equations 93 (1991), 62-101.
24. I. Lasiecka and R. Triggiani, Regularity theory for a class of non-homogeneous Euler-Bernoulli equations: A cosine operator approach, Boll. Un. Mat. Ital. 3-B (1989), 199-228.
25. I. Lasiecka and R. Triggiani, Sharp trace estimates of solutions to Kirchhoff and Euler-Bernoulli equations, Appl. Math. Optim. 28 (1993), 277-306.
26. A. Pazy, "Semigroups of Operators and Applications to Partial Differential Equations," Springer-Verlag, Berlin/New York, 1983.
27. P(0, T; B), Ann. Mat. Pura Appl. (4) CXLVI (1987), 65-96.
28. M. A. Horn, Uniform decay rates for the solutions to the Euler Bernoulli plate equation with boundary feedback via benoling moments, Differential, Integral Equations, 6(5), (1992), 1121-1150.