Displaying similar documents to “Stabilization and control for the subcritical semilinear wave equation”

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...

Well posedness and control of semilinear wave equations with iterated logarithms

Piermarco Cannarsa, Vilmos Komornik, Paola Loreti (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Motivated by a classical work of Erdős we give rather precise necessary and sufficient growth conditions on the nonlinearity in a semilinear wave equation in order to have global existence for all initial data. Then we improve some former exact controllability theorems of Imanuvilov and Zuazua.

Exact controllability of the radial solutions of the semilinear wave equation in R.

Luz de Teresa (1998)

Revista Matemática Complutense

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The exact internal controllability of the radial solutions of a semilinear heat equation in R is proved. The result applies for nonlinearities that are of an order smaller than |s| logp |s| at infinity for 1 ≤ p < 2. The method of the proof combines HUM and a fixed point technique.