Uniform energy decay rates of hyperbolic equations with nonlinear boundary and interior dissipation
Irena Lasiecka, Roberto Triggiani (2008)
Control and Cybernetics
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Irena Lasiecka, Roberto Triggiani (2008)
Control and Cybernetics
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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...
Bucci, F., Lasiecka, I., Triggiani, R. (2002)
Abstract and Applied Analysis
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Lasiecka, Irena, Triggiani, Roberto (1998)
Abstract and Applied Analysis
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Gimyong Hong, Hakho Hong (2022)
Applications of Mathematics
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We are concerned with a transmission problem for the Kirchhoff plate equation where one small part of the domain is made of a viscoelastic material with the Kelvin-Voigt constitutive relation. We obtain the logarithmic stabilization result (explicit energy decay rate), as well as the wellposedness, for the transmission system. The method is based on a new Carleman estimate to obtain information on the resolvent for high frequency. The main ingredient of the proof is some careful analysis...
Najafi, Mahmoud (2001)
International Journal of Mathematics and Mathematical Sciences
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Kais Ammari, Marius Tucsnak (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.