Displaying similar documents to “Decay of solutions of a nonlinear hyperbolic system in noncylindrical domain.”

Global in time solvability of the initial boundary value problem for some nonlinear dissipative evolution equations

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.

A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations

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...