On a nonlinear wave equation in unbounded domains.
Vasconcellos, Carlos Frederico (1988)
International Journal of Mathematics and Mathematical Sciences
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Vasconcellos, Carlos Frederico (1988)
International Journal of Mathematics and Mathematical Sciences
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Muñoz Rivera, Jaime E. (1994)
International Journal of Mathematics and Mathematical Sciences
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Ferreira, Jorge, Pereira, Ducival Carvalho (1992)
International Journal of Mathematics and Mathematical Sciences
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L. A. Medeiros, M. Milla Miranda (1990)
Revista Matemática de la Universidad Complutense de Madrid
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Clark, Marcondes Rodrigues (1996)
International Journal of Mathematics and Mathematical Sciences
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Smiley, M.W., Fink, A.M. (1990)
International Journal of Mathematics and Mathematical Sciences
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Ferreira, Jorge (1996)
International Journal of Mathematics and Mathematical Sciences
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Ebihara, Y, Pereira, D.C. (1989)
International Journal of Mathematics and Mathematical Sciences
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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.
Akkouchi, Mohamed, Bounabat, Abdellah (2003)
Mathematica Pannonica
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Louis Tebou (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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First, we consider a semilinear hyperbolic equation with a locally distributed damping in a bounded domain. The damping is located on a neighborhood of a suitable portion of the boundary. Using a Carleman estimate [Duyckaerts, Zhang and Zuazua, Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear); Fu, Yong and Zhang, SIAM J. Contr. Opt. 46 (2007) 1578–1614], we prove that the energy of this system decays exponentially to zero as the time variable goes to infinity. Second, relying on...