References
- Zuazua E. Exponential decay for the semilinear wave equation with locally distributed damping. Commun Partial Differ Equa. 1990;15:205–235.
- Komornik V. Decay estimates for the wave equation with internal damping. Int Ser Numer Math. 1994;118:253–266.
- Nakao M. Decay of solutions of the wave equation with a local nonlinear dissipation. Math Ann. 1996;305:403–417.
- Komornik V, Zuazua E. A direct method for the boundary stabilization of the wave equation. J Math Pures Appl. 1990;69:33–54.
- Lasiecka I. Global uniform decay rates for the solution to the wave equation with nonlinear boundary conditions. Appl Anal. 1992;47:191–212.
- Lasiecka I. Stabilization of wave and plate-like equations with nonlinear dissipation on the boundary. J Differ Equa. 1989;79:340–381.
- Zuazua E. Uniform stabilization of the wave equation by nonlinear boundary feedback. SIAM J Control Optim. 1990;28(2):466–477.
- Benaissa A, Mimouni S. Energy decay of solutions of a wave equation of p-Laplacian type with a weakly nonlinear dissipation. J Inequal Pure Appl Math. 2006;7(1):Article 15, 8 p.
- Lasiecka I, Tataru D. Uniform boundary stabilization of semilinear wave equation with nonlinear boundary damping. Differ Integral Equa. 1993;8:507–533.
- Liu W-J, Zuazua E. Decay rates for dissipative wave equations. Ricerche Mat. 1999;48:61–75.
- Lasiecka I, Toundykov D. Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms. Nonlinear Anal. 2006;64:1757–1797.
- Lasiecka I, Toundykov D. Regularity of higher energies of wave equation with nonlinear localized damping and a nonlinear source. Nonlinear Anal. 2008;69:898–910.
- Cavalcanti MM, Domingos Cavalcanti VN, Lasiecka I. Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction. J Differ Equa. 2007;236:407–459.
- Bchatnia A, Daoulatli M. Local energy decay for the wave equation with a nonlinear time-dependent damping. Appl Anal. 2013;92(11):2288–2308.
- Daoulatli M. Rates of decay for the wave systems with time dependent damping. Discrete Contin Dyn Syst. 2011;31(2):407–443.
- Martinez P. A new method to decay rate estimates for dissipative systems. ESAIM Control Optim Calc Var. 1999;4:419–444.
- Martinez P. A new method to obtain decay rate estimates for dissipative systems with localized damping. Rev Mat Complut. 1999;12(1):251–283.
- Liu K. Locally distributed control and damping for the conservative systems. SIAM J Control Optim. 1997;35:1574–1590.
- Alabau-Boussouira F. Convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems. Appl Math Optim. 2005;51:61–105.
- Cavalcanti MM, Domingos Cavalcanti VN, Martinez P. General decay rate estimates for viscoelastic dissipative systems. Nonlinear Anal. 2008;68(1):177–193.
- Messaoudi SA, Mustafa MI. On the control of solutions of viscoelastic equations with boundary feedback. Nonlinear Anal Real World Appl. 2009;10:3132–3140.
- Arnold VI. Mathematical methods of classical mechanics. New York (NY): Springer-Verlag; 1989.