Displaying similar documents to “Boundary stabilization of the Schrödinger equation in almost star-shaped domain”

Boundary stabilization of Maxwell’s equations with space-time variable coefficients

Serge Nicaise, Cristina Pignotti (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the stabilization of Maxwell’s equations with space-time variable coefficients in a bounded region with a smooth boundary by means of linear or nonlinear Silver–Müller boundary condition. This is based on some stability estimates that are obtained using the “standard” identity with multiplier and appropriate properties of the feedback. We deduce an explicit decay rate of the energy, for instance exponential, polynomial or logarithmic decays are available for appropriate feedbacks. ...

Boundary stabilization of Maxwell's equations with space-time variable coefficients

Serge Nicaise, Cristina Pignotti (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider the stabilization of Maxwell's equations with space-time variable coefficients in a bounded region with a smooth boundary by means of linear or nonlinear Silver–Müller boundary condition. This is based on some stability estimates that are obtained using the “standard" identity with multiplier and appropriate properties of the feedback. We deduce an explicit decay rate of the energy, for instance exponential, polynomial or logarithmic decays are available for appropriate feedbacks. ...

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...

Unique continuation and decay for the Korteweg-de Vries equation with localized damping

Ademir Fernando Pazoto (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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This work is devoted to prove the exponential decay for the energy of solutions of the Korteweg-de Vries equation in a bounded interval with a localized damping term. Following the method in Menzala (2002) which combines energy estimates, multipliers and compactness arguments the problem is reduced to prove the unique continuation of weak solutions. In Menzala (2002) the case where solutions vanish on a neighborhood of both extremes of the bounded interval where equation holds was solved...