Decacy of solutions of the wave equation with a local nonlinear dissipation.
Mitsuhiro Nakao (1996)
Mathematische Annalen
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Mitsuhiro Nakao (1996)
Mathematische Annalen
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Mitsuhiro Nakao (1991)
Mathematische Zeitschrift
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Mitsuhiro Nakao (1986)
Mathematische Zeitschrift
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Benaissa, Abbes, Messaoudi, Salim A. (2002)
Journal of Applied Mathematics
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Jianwei Yang (2011)
Applicationes Mathematicae
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We study the initial-boundary problem for a nonlinear system of wave equations with Hamilton structure under Dirichlet's condition. We use the local-in-time Strichartz estimates from [Burq et al., J. Amer. Math. Soc. 21 (2008), 831-845], Morawetz-Pohožaev's identity derived in [Miao and Zhu, Nonlinear Anal. 67 (2007), 3136-3151], and an a priori estimate of the solutions restricted to the boundary to show the existence of global and unique solutions.
Robert T. Glassey (1981)
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.
J.M. Coron (1983)
Mathematische Annalen
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Hiroyuki Takamura (1994)
Mathematische Zeitschrift
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Wolf von Wahl, Philip Brenner (1981)
Mathematische Zeitschrift
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Robert T. Glassey (1973)
Mathematische Zeitschrift
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