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Keywords:
wave equation; integral inequality; damping and source terms; uniform stabilization; energy decay
wave equation; integral inequality; damping and source terms; uniform stabilization; energy decay
Summary:
In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms.
References:
[1] Hosoya M., Yamada Y.: On some nonlinear wave equations 1: local existence and regularity of solutions. J. Fac. Sci .Univ. Tokyo Sect.IA, Math. 38 (1991), 225-238. MR 1127081
[2] Hosoya M., Yamada Y.: On some nonlinear wave equations 2: global existence and energy decay of solutions. J. Fac. Sci. Univ. Tokyo Sect.IA, Math. 38 (1991), 239-250. MR 1127082
[3] Ikehata R.: A note on the global solvability of solutions to some nonlinear wave equations with dissipative terms. Differential and Integral Equations 8(3) (1995), 607-616. MR 1306578 | Zbl 0812.35081
[4] Komornik V.: Exact Controllability and Stabilization. The Multiplier Method. Masson-John Wiley, Paris, 1994. MR 1359765 | Zbl 0937.93003
[5] Lions J.L.: Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires. Dunod, Paris, 1969. MR 0259693 | Zbl 0248.35001
[6] Payne L.E., Sattinger D.H.: Saddle points and unstability of nonlinear hyperbolic equations. Israel J. Math. 22 (1975), 273-303. MR 0402291
[7] Sattinger D.H.: On global solution of nonlinear hyperbolic equations. Arch. Rational Mech. Anal. 30 (1968), 148-172. MR 0227616 | Zbl 0159.39102
[8] Tsutsumi M.: On solutions of semilinear differential equations in a Hilbert space. Math. Japon. 17 (1972), 173-193. MR 0355247 | Zbl 0273.34044
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