Cavalcanti, M. M.; Domingos Cavalcanti, V. N.; Soriano, J. A. On existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions. (English) Zbl 1026.35084 J. Math. Anal. Appl. 281, No. 1, 108-124 (2003). The authors prove existence of regular and weak solutions of a degenerate wave equation subject to nonlinear boundary conditions. Under additional assumptions they obtain uniform decay of solutions. Reviewer: Marie Kopáčková (Praha) Cited in 16 Documents MSC: 35L80 Degenerate hyperbolic equations 35B40 Asymptotic behavior of solutions to PDEs 35L20 Initial-boundary value problems for second-order hyperbolic equations 35L70 Second-order nonlinear hyperbolic equations Keywords:global solvability; nonlinear boundary damping; stabilization; exponential decay PDFBibTeX XMLCite \textit{M. M. Cavalcanti} et al., J. Math. Anal. Appl. 281, No. 1, 108--124 (2003; Zbl 1026.35084) Full Text: DOI References: [1] Cavalcanti, M. M.; Domingos Cavalcanti, V. N.; Medeiros, L. A.; Soriano, J. A., On existence and uniform decay of a hyperbolic equation with nonlinear boundary conditions, Southeast Asian Bull. Math., 24, 183-199 (2000) · Zbl 0953.35086 [2] Cavalcanti, M. M.; Domingos Cavalcanti, V. N.; Prates Filho, J. S.; Soriano, J. A., Existence and uniform decay of solutions of the degenerate equation with nonlinear boundary damping and boundary memory source term, Nonlinear Anal., 38, 281-294 (1999) · Zbl 0933.35157 [3] Cavalcanti, M. M.; Domingos Cavalcanti, V. N., On solvability of solutions of degenerate nonlinear equations on manifolds, Differential Integral Equations, 13, 1445-1458 (2000) · Zbl 0979.35003 [4] Chen, G., A note on the boundary stabilization of the wave equation, SIAM J. Control Optim., 19, 107-113 (1981) [5] Chen, G., Control and stabilization for the wave equation in a bounded domain, SIAM J. Control Optim., 17, 114-122 (1979) [6] Chen, G., Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain, J. Math. Pures Appl., 58, 249-273 (1979) · Zbl 0414.35044 [7] Conrad, F.; Rao, B., Decay of solutions of the wave equation in a star-shaped domain with nonlinear boundary feedback, Asymptotic Anal., 7, 159-177 (1993) · Zbl 0791.35011 [8] Komornik, V.; Rao, Boundary stabilization of compactly coupled wave equations, Asymptotic Anal., 14, 339-359 (1997) · Zbl 0887.35088 [9] Komornik, V.; Zuazua, E., A direct method for boundary stabilization of the wave equation, J. Math. Pures Appl., 69, 33-54 (1990) · Zbl 0636.93064 [10] Lagnese, J. E., Decay of solution of wave equations in a bounded region with boundary dissipation, J. Differential Equations, 50, 163-182 (1983) · Zbl 0536.35043 [11] Lagnese, J. E., Note on boundary stabilization of wave equations, SIAM J. Control Optim., 26, 1250-1257 (1988) · Zbl 0657.93052 [12] Lasiecka, I.; Tataru, D., Uniform boundary stabilization of semilinear wave equation with nonlinear boundary damping, Differential Integral Equations, 6, 507-533 (1993) · Zbl 0803.35088 [13] Lions, J. L., Quelques Méthodes de Résolution des Problémes aux Limites non Linéaires (1969), Dunod: Dunod Paris · Zbl 0189.40603 [14] Quinn, J.; Russel, D. L., Asymptotic stability and energy decay for solutions of hyperbolic equations, with boundary damping, Proc. Roy. Soc. Edinburgh Sect. A, 77, 97-127 (1987) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.