On the global solvability of solutions to a quasilinear wave equation with localized damping and source terms.
Cabanillas Lapa, E., Huaringa Segura, Z., Leon Barboza, F. (2005)
Journal of Applied Mathematics
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Cabanillas Lapa, E., Huaringa Segura, Z., Leon Barboza, F. (2005)
Journal of Applied Mathematics
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Ye, Yaojun (2010)
Journal of Inequalities and Applications [electronic only]
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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...
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.
Yu, Shengqi (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Benaissa, Abbes, Messaoudi, Salim A. (2002)
Journal of Applied Mathematics
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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.
Benaissa, Abbès, Mokeddem, Soufiane (2004)
Abstract and Applied Analysis
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Ye, Yaojun (2010)
Journal of Inequalities and Applications [electronic only]
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Ye, Yaojun (2010)
Advances in Difference Equations [electronic only]
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