Stabilization of trajectories for some weakly damped hyperbolic equations
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In this paper, the authors study the phenomenon of stabilisation of trajectories for a wave equation in a bounded open domain, endowed with a weak dissipative mechanism, and show that the self-oscillations induced by the wave equation are damped out asymptotically and so we are left, when time tends to infinity, either with an equilibrium if the system is autonomous, or with a forced oscillation if it was submitted to an exterior, periodic or almost periodic excitation.About:
This article is published in Journal of Differential Equations.The article was published on 1985-09-15 and is currently open access. It has received 104 citations till now. The article focuses on the topics: Hyperbolic partial differential equation & Dissipative system.read more
Citations
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Exponential decay for the semilinear wave equation with locally distributed damping
TL;DR: In this article, the exponential decay for the Semilinear Wave Equation with Locally Distributed Damping is investigated. But the decomposition is not considered in this paper, as it is in this article.
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Stabilisation de l’équation des ondes par le bord
Gilles Lebeau,Luc Robbiano +1 more
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Stabilization of the Korteweg-De Vries equation with localized damping
TL;DR: In this paper, the stabilization of solutions of the Korteweg-de Vries (KdV) equation in a bounded interval under the effect of a localized damping mechanism is studied.
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Stabilization and control for the subcritical semilinear wave equation
TL;DR: In this paper, the authors analyzed the exponential decay property of solutions of the semilinear wave equation in R3 with a damping term which is effective on the exterior of a ball.
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Weighted L2-estimates for dissipative wave equations with variable coefficients
TL;DR: In this paper, the authors established weighted L 2 -estimates for the wave equation with variable damping u t t t − Δ u + a u t = 0 in R n, where a (x ) ⩾ a 0 ( 1 + | x | ) − α with a 0 > 0 and α ∈ [ 0, 1 ] ∈ the [ 0, 1 ] subspace.
References
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Book
Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert
TL;DR: In this article, Operateurs Maximaux Monotones: Et Semi-Groupes De Contractions Dans Les Espaces De Hllbert are described and discussed. But the focus is not on the performance of the operators.
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Asymptotic behavior of nonlinear contraction semigroups
TL;DR: In this article, the asymptotic behavior of weak solutions of weak contraction semigroup is characterized via a characterization of ω-limit sets of the contraction semiigroup generated by −A.
Book
Nonlinear Evolution Equations - Global Behavior of Solutions
TL;DR: In this paper, the authors consider quasi-periodic quasi-autonomous dissipative systems in a Hilbert space and show asymptotic behavior for solutions of the nonlinear dissipative forced wave equation.
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Asymptotic Behavior of Solutions of Evolution Equations
TL;DR: In this paper, the authors present the methods of investigation of the asymptotic behavior of solutions of evolution equations, endowed with a dissipative mechanism, based on the study of the structure of the ω-limit set of trajectories of the evolution operator generated by the equation.
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On a uniqueness theorem of L. Amerio and G. Prouse
TL;DR: In this paper, two generalizations of Amerio and Prouse's theorem concerning uniqueness of the almost-periodic solution of the wave equation with a local multivalued damping term were presented.