Finite-Time Blow-Up for Solutions of Nonlinear Wave Equations.
Robert T. Glassey (1981)
Mathematische Zeitschrift
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Robert T. Glassey (1981)
Mathematische Zeitschrift
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Robert T. Glassey (1973)
Mathematische Zeitschrift
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Mitsuhiro Nakao (1991)
Mathematische Zeitschrift
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Mitsuhiro Nakao (1986)
Mathematische Zeitschrift
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Fritz John (1979)
Manuscripta mathematica
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Benaissa, Abbes, Messaoudi, Salim A. (2002)
Journal of Applied Mathematics
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Wolf von Wahl, Philip Brenner (1981)
Mathematische Zeitschrift
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Vladimir Georgiev (1990)
Mathematische Zeitschrift
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Rentaro Agemi (1991)
Manuscripta mathematica
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Yoshihiro Shibata, Yoshio Tsutsumi (1986)
Mathematische Zeitschrift
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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.
Lorena Bociu, Irena Lasiecka (2008)
Applicationes Mathematicae
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We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove that under specific conditions relating the sources and the dissipations (namely p > m and k > m), weak solutions blow up in finite time.
Wolf von Wahl (1975)
Mathematische Zeitschrift
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