The asymptotic behavior of the linear transmission problem in viscoelasticity

Margareth Alves, Jaime Muñoz Rivera, Mauricio Sepúlveda, Octavio Vera Villagrán, María Zegarra Garay

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

We consider a transmission problem with localized Kelvin-Voigt viscoelastic damping. Our main result is to show that the corresponding semigroup (SA(t))t≥0 is not exponentially stable, but the solution of the system decays polynomially to zero as 1/t2 when the initial data are taken over the domain D(A). Moreover, we prove that this rate of decay is optimal. Finally, using a second order scheme that ensures the decay of energy (Newmark-β method), we give some numerical examples which demonstrate this polynomial asymptotic behavior. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Original languageAmerican English
Pages (from-to)483-497
Number of pages15
JournalMathematische Nachrichten
DOIs
StatePublished - 1 Jan 2014

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