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A new method to obtain decay rate estimates for dissipative systems

Published online by Cambridge University Press:  15 August 2002

Patrick Martinez
Patrick Martinez*
Affiliation:
Département de Mathématiques, ENS Cachan, Antenne de Bretagne and IRMAR, Université Rennes I, Campus de Ker Lann, 35170 Bruz, France; martinez@bretagne.ens-cachan.fr.
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Abstract

We consider the wave equation damped with a boundary nonlinear velocity feedback p(u'). Under some geometrical conditions, we prove that the energy of the system decays to zero with an explicit decay rate estimate even if the function ρ has not a polynomial behavior in zero. This work extends some results of Nakao, Haraux, Zuazua and Komornik, who studied the case where the feedback has a polynomial behavior in zero and completes a result of Lasiecka and Tataru. The proof is based on the construction of a special weight function (that depends on the behavior of the function ρ in zero), and on a new nonlinear integral inequality.

Keywords

Nonlinear stabilizationasymptotic behavior in zero and at infinity.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 4 , 1999 , pp. 419 - 444
Copyright
© EDP Sciences, SMAI, 1999

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