Regular Solutions of Initial-Boundary Value-Problems for Linear and Nonlinear Wave-Equations. II.
Wolf von Wahl (1975)
Mathematische Zeitschrift
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Wolf von Wahl (1975)
Mathematische Zeitschrift
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Rentaro Agemi (1991)
Manuscripta mathematica
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Hartmut Pecher, Robert Glassey (1982)
Manuscripta mathematica
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Fritz John (1979)
Manuscripta mathematica
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Alain Haraux (1985)
Manuscripta mathematica
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Mitsuhiro Nakao (1986)
Mathematische Zeitschrift
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Paul H. Rabinowitz (1971)
Manuscripta mathematica
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Klaus-Jürgen Eckardt (1976)
Manuscripta mathematica
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Peter Weidemaier (1986)
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.
Mitsuhiro Nakao (1991)
Mathematische Zeitschrift
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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.
Petronela Radu (2008)
Applicationes Mathematicae
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We show local existence of solutions to the initial boundary value problem corresponding to a semilinear wave equation with interior damping and source terms. The difficulty in dealing with these two competitive forces comes from the fact that the source term is not a locally Lipschitz function from H¹(Ω) into L²(Ω) as typically assumed in the literature. The strategy behind the proof is based on the physics of the problem, so it does not use the damping present in the equation. The...
Jeng-Eng Lin (1979/80)
Manuscripta mathematica
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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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