Journal Article

Exponential stability of second-order evolution equations with structural damping and dynamic boundary delay feedback

Serge Nicaise and Cristina Pignotti

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 28, issue 4, pages 417-446
Published in print December 2011 | ISSN: 0265-0754
Published online June 2011 | e-ISSN: 1471-6887 | DOI: https://dx.doi.org/10.1093/imamci/dnr012
Exponential stability of second-order evolution equations with structural damping and dynamic boundary delay feedback

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We consider a stabilization problem for abstract second-order evolution equations with dynamic boundary feedback laws with a delay and distributed structural damping. We prove an exponential stability result under a suitable condition between the internal damping and the boundary laws. The proof of the main result is based on an identity with multipliers that allows to obtain a uniform decay estimate for a suitable energy functional. Some concrete examples are detailed. Some counterexamples suggest that this condition is optimal.

Keywords: second-order evolution equations; wave equation; delay feedbacks; stabilization

Journal Article.  0 words. 

Subjects: Mathematics

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