Displaying similar documents to “Stabilization of second order evolution equations with unbounded feedback with delay”

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...

Stabilization of the wave equation by on-off and positive-negative feedbacks

Patrick Martinez, Judith Vancostenoble (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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Motivated by several works on the stabilization of the oscillator by on-off feedbacks, we study the related problem for the one-dimensional wave equation, damped by an on-off feedback a ( t ) u t . We obtain results that are radically different from those known in the case of the oscillator. We consider periodic functions a : typically a is equal to 1 on ( 0 , T ) , equal to 0 on ( T , q T ) and is q T -periodic. We study the boundary case and next the locally distributed case, and we give optimal results of stability....

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. ...