Uniform stabilization of a coupled structural acoustic system by boundary dissipation.
Camurdan, Mehmet (1998)
Abstract and Applied Analysis
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Camurdan, Mehmet (1998)
Abstract and Applied Analysis
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Bucci, F., Lasiecka, I., Triggiani, R. (2002)
Abstract and Applied Analysis
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Martinez, P., Vancostenoble, J. (2000)
Portugaliae Mathematica
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Nicaise, S. (2003)
Portugaliae Mathematica. Nova Série
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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...
Abdoua Tchousso, Thibaut Besson, Cheng-Zhong Xu (2009)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov’s second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering...
Arnaud Münch, Ademir Fernando Pazoto (2007)
ESAIM: Control, Optimisation and Calculus of Variations
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This work is devoted to the analysis of a viscous finite-difference space semi-discretization of a locally damped wave equation in a regular 2-D domain. The damping term is supported in a suitable subset of the domain, so that the energy of solutions of the damped continuous wave equation decays exponentially to zero as time goes to infinity. Using discrete multiplier techniques, we prove that adding a suitable vanishing numerical viscosity term leads to a uniform (with respect to the...
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...