Logarithmic stabilization of the Euler Bernoulli transmission plate equation with locally distributed Kelvin-Voigt damping

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Hassine, Fathi¹ 

[1] Univ Monastir, Fac Sci Monastir, Dept Math, UR Anal & Control PDE UR13ES64, Monastir 5019, Tunisia

关键词: Transmission problem;    Kelvin-Voigt damping;    Euler-Bernoulli plate equation;    Energy decay;    Carleman estimates;   

DOI  :  10.1016/j.jmaa.2017.06.068

来源: Elsevier

【 摘 要 】

In this work we consider a transmission problem for a plate equation where one small part of the domain is made of a viscoelastic material with Kelvin-Voigt constitutive relation. We apply the general results due to Burg's [10] in the study of asymptotic behavior of solutions and prove that the semigroup associated to the system is logarithmically stable. The main ingredient of the proof is the Carleman estimates. The method consist to use Carleman estimates to obtain information on the resolvent for high frequency. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free