On the Decay of Solutions of Some Nonlinear Dissipative Wave Equations in Higher Dimensions.
Mitsuhiro Nakao (1986)
Mathematische Zeitschrift
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Mitsuhiro Nakao (1986)
Mathematische Zeitschrift
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Robert T. Glassey (1981)
Mathematische Zeitschrift
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Wolf von Wahl, Philip Brenner (1981)
Mathematische Zeitschrift
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Hiroyuki Takamura (1994)
Mathematische Zeitschrift
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Robert T. Glassey (1973)
Mathematische Zeitschrift
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Benaissa, Abbes, Messaoudi, Salim A. (2002)
Journal of Applied Mathematics
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T. Koboyashi, H. Pecher, Y. Shibata (1993)
Mathematische Annalen
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Yoshihiro Shibata, Yoshio Tsutsumi (1986)
Mathematische Zeitschrift
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Haraux, A. (1992)
Portugaliae mathematica
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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.
Fritz John (1979)
Manuscripta mathematica
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Wolf von Wahl (1975)
Mathematische Zeitschrift
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Aissa Guesmia (1998)
Annales Polonici Mathematici
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We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.