Abstract
We study the global existence, uniqueness, and asymptotic behavior of solutions for a class of generalized plate-membrane-like systems with nonlinear damping and source acting both interior and on boundary.
We study the global existence, uniqueness, and asymptotic behavior of solutions for a class of generalized plate-membrane-like systems with nonlinear damping and source acting both interior and on boundary.
M. Aassila, “A note on the boundary stabilization of a compactly coupled system of wave equations,” Applied Mathematics Letters, vol. 12, no. 3, pp. 19–24, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. Aassila, M. M. Cavalcanti, and J. A. Soriano, “Asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star-shaped domain,” SIAM Journal on Control and Optimization, vol. 38, no. 5, pp. 1581–1602, 2000.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. J. Bae, “On uniform decay of the solution for a damped nonlinear coupled system of wave equations with nonlinear boundary damping and memory term,” Applied Mathematics and Computation, vol. 148, no. 1, pp. 207–223, 2004.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. M. Cavalcanti, V. N. Domingos Cavalcanti, J. S. Prates Filho, and J. A. Soriano, “Existence and exponential decay for a Kirchhoff-Carrier model with viscosity,” Journal of Mathematical Analysis and Applications, vol. 226, no. 1, pp. 40–60, 1998.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. M. Cavalcanti, V. N. Domingos Cavalcanti, J. S. Prates Filho, and J. A. Soriano, “Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping,” Differential and Integral Equations, vol. 14, no. 1, pp. 85–116, 2001.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. M. Choo and S. K. Chung, “Finite difference approximate solutions for the strongly damped extensible beam equations,” Applied Mathematics and Computation, vol. 112, no. 1, pp. 11–32, 2000.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetV. Georgiev and G. Todorova, “Existence of a solution of the wave equation with nonlinear damping and source terms,” Journal of Differential Equations, vol. 109, no. 2, pp. 295–308, 1994.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. Guesmia, “Energy decay for a damped nonlinear coupled system,” Journal of Mathematical Analysis and Applications, vol. 239, no. 1, pp. 38–48, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. Jiang and J. E. Muñoz Rivera, “A global existence theorem for the Dirichlet problem in nonlinear -dimensional viscoelasticity,” Differential and Integral Equations, vol. 9, no. 4, pp. 791–810, 1996.
View at: Google Scholar | Zentralblatt MATH | MathSciNetV. Komornik and P. Loreti, “Ingham-type theorems for vector-valued functions and observability of coupled linear systems,” SIAM Journal on Control and Optimization, vol. 37, no. 2, pp. 461–485, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetV. Komornik and E. Zuazua, “A direct method for the boundary stabilization of the wave equation,” Journal de Mathématiques Pures et Appliquées. Neuvième Série, vol. 69, no. 1, pp. 33–54, 1990.
View at: Google Scholar | Zentralblatt MATH | MathSciNetT. F. Ma, “Existence results and numerical solutions for a beam equation with nonlinear boundary conditions,” Applied Numerical Mathematics, vol. 47, no. 2, pp. 189–196, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetZ. Oniszczuk, “Free transverse vibrations of an elastically connected rectangular plate-membrane complex system,” Journal of Sound and Vibration, vol. 264, no. 1, pp. 37–47, 2003.
View at: Publisher Site | Google ScholarR. E. Showalter, Monotone operators in Banach space and nonlinear partial differential equations, vol. 49 of Mathematical Surveys and Monographs, American Mathematical Society, Rhode Island, 1997.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Soufyane, “Uniform stability of displacement coupled second-order equations,” Electronic Journal of Differential Equations, vol. 2001, no. 25, pp. 1–10, 2001.
View at: Google Scholar | Zentralblatt MATH | MathSciNetE. Vitillaro, “Global existence for the wave equation with nonlinear boundary damping and source terms,” Journal of Differential Equations, vol. 186, no. 1, pp. 259–298, 2002.
View at: Publisher Site | Google Scholar | MathSciNet