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 journalArticlepeer-review

20 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.

Original languageEnglish
Pages (from-to)483-497
Number of pages15
JournalMathematische Nachrichten
Volume287
Issue number5-6
DOIs
StatePublished - Apr 2014

Keywords

  • Kelvin-Voigt
  • Newmark-β method
  • Polynomial decay
  • Semigroup
  • Transmission problem
  • Viscoelastic damping

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