Displaying similar documents to “Stabilization of the Schrödinger equation.”

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. ...

Stabilization of Berger–Timoshenko’s equation as limit of the uniform stabilization of the von Kármán system of beams and plates

G. Perla Menzala, Ademir F. Pazoto, Enrique Zuazua (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter ε > 0 and study its asymptotic behavior for t large, as ε → 0 . Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter ε . In order for this to be true the damping mechanism has to have the appropriate scale with respect to ε . In the limit as ε → 0 we obtain damped Berger–Timoshenko...

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...

Boundary stabilization of the linear elastodinamic system by a Lyapunov-type method.

Rabah Bey, Amar Heminna, Jean-Pierre Lohéac (2003)

Revista Matemática Complutense

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We propose a direct approach to obtain the boundary stabilization of the isotropic linear elastodynamic system by a natural feedback; this method uses local coordinates in the expression of boundary integrals as a main tool. It leads to an explicit decay rate of the energy function and requires weak geometrical conditions: for example, the spacial domain can be the difference of two star-shaped sets.