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Asymptotic Behaviour to a Von Kármán System with Internal Damping
Departament of Mathematics, Pará State University, UEPA, Belém, Brazil
Departament of Mathematics, Federal University of S?o Jo?o Del-Rei, UFSJ, S?o Jo?o Del-Rei, Brazil
Departament of Mathematics, Federal University of Pará, UFPA, Belém, Brazil
- 1 Departament of Mathematics, Pará State University, UEPA, Belém, Brazil
- 2 Departament of Mathematics, Federal University of S?o Jo?o Del-Rei, UFSJ, S?o Jo?o Del-Rei, Brazil
- 3 Departament of Mathematics, Federal University of Pará, UFPA, Belém, Brazil
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Abstract
In this work we consider the Von Kármán system with internal damping acting on the displacement of the plate and using the Theorem due to Nakao [1] we prove the exponential decay of the solution.
KeywordsVon Kármán SystemInternal DampingExponential DecayTheorem of Nakao
- M. Nakao, “A Difference Inequalit and Its Application to Nonolinear Evolution Equation,” Journal of the Mathematical Society of Japan, Vol. 30, No. 4, 1978, pp. 747-762. doi:10.2969/jmsj/03040747
- T. V. Kármán, “Festigkeitsprobleme im Maschinenbaum. Encyklopadie der Math,” Wiss. V/4C, Leipzig, 1910, pp. 311-385.
- M. Horn and I. Lasiecka, “Uniform Decay of Weak Solutions to a Von Kármán Plate with Nonlinear Boundary Dissipation,” Differential and Integral Equations, Vol. 7, No. 4, 1994, pp. 885-908.
- M. Horn and I. Lasiecka, “Global Stabilization of a Dynamical Von Kármán Plate with Nonlinear Boundary Feedback,” Applied Mathematics & Optimization, Vol. 31, No. 1, 1995, pp. 57-84. doi:10.1007/BF01182557
- M. Horn, A. Favini, I. Lasiecka and D. Tataru, “Global Existence, Uniqueness and Regularity to a Von Kármán System with Nonlinear Boundary Dissipation,” Differential and Integral Equations, Vol. 9, No. 2, 1996, pp. 267-294.
- G. P. Menzala and E. Zuazua, “Energy Decay Rates for the Von Kármán System of Thermoelastic Plates,” Differential and Integral Equations, Vol. 11, No. 5, 1998, pp. 755-770.
- J. E. M. Rivera and G. P. Menzala, “Decay Rates of Solutions of a Von Kármán System for Viscoelastic Plates with Memory,” Quarterly of Applied Mathematics, Estados Unidos, Vol. 82, No. 1, 1999, pp.181-200.
- J. E. M. Rivera, H. P. Oquendo and M. L. Santos, “Asymptotic Behavior to a Von Kármán Plate with Boundary Memory Conditions,” Nonlinear Analysis, Vol. 62, No. 7, 2005, pp. 1183-1205. doi:10.1016/j.na.2005.04.025
- C. A. Raposo and M. L. Santos, “General Decay to a Von Kármán System with Memory,” Nonlinear Analysis, Vol. 74, No. 3, 2011, pp. 937 945. doi:10.1016/j.na.2010.09.047
- G. Avalos and I. Lasiecka, “Uniform Decays in Nonlinear Thermoelastic System,” In: W. Hager and P. Pardalos, Eds., Optimal Control, Theory Algorithms and Application, Kluwer, 1998, pp. 1-23.
- G. Avalos, I. Lasiecka and R. Triggiani, “Uniform Stability of Nonlinear Thermoelastic Plates with Free Boundary Conditions,” International Series of Numerical Mathematics, Vol. 133, 1999, pp. 13-32.
- H. Koch and A. Stahel, “Global Existence of Classical Solutions to the Dynamical Von Kármán Equations,” Mathematical Methods in the Applied Sciences, Vol. 161, 1993, pp. 581-586. doi:10.1002/mma.1670160806
- J. Puel and M. Tucsnak, “Boundary Stabilization for the Von Kármán Equations,” SIAM Journal on Control and Optimization, Vol. 33, No. 1, 1996, pp. 255-273. doi:10.1137/S0363012992228350