Blowup of solutions of a nonlinear wave equation.
Benaissa, Abbes, Messaoudi, Salim A. (2002)
Journal of Applied Mathematics
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Benaissa, Abbes, Messaoudi, Salim A. (2002)
Journal of Applied Mathematics
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Yang Zhifeng (2008)
Open Mathematics
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The initial boundary value problem for a viscoelastic equation with nonlinear damping in a bounded domain is considered. By modifying the method, which is put forward by Li, Tasi and Vitillaro, we sententiously proved that, under certain conditions, any solution blows up in finite time. The estimates of the life-span of solutions are also given. We generalize some earlier results concerning this equation.
L. A. Medeiros, M. Milla Miranda (1990)
Revista Matemática de la Universidad Complutense de Madrid
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Haraux, A. (1992)
Portugaliae mathematica
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Wu, Shun-Tang, Tsai, Long-Yi (2006)
Applied Mathematics E-Notes [electronic only]
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J. M. Ghidaglia, R. Temam (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Mitsuhiro Nakao (1991)
Mathematische Zeitschrift
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Yoshihiro Shibata (1993)
Commentationes Mathematicae Universitatis Carolinae
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The global in time solvability of the one-dimensional nonlinear equations of thermoelasticity, equations of viscoelasticity and nonlinear wave equations in several space dimensions with some boundary dissipation is discussed. The blow up of the solutions which might be possible even for small data is excluded by allowing for a certain dissipative mechanism.