Stabilization of second order evolution equations with unbounded feedback with time-dependent delay

Emilia Fridman*, Serge Nicaise, Julie Valein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

57 Scopus citations

Abstract

We consider abstract second order evolution equations with unbounded feedback with time-varying delay. Existence results are obtained under some realistic assumptions. We prove the exponential decay under some conditions by introducing an abstract Lyapunov functional. Our abstract framework is applied to the wave, to the beam, and to the plate equations with boundary delays.

Original languageEnglish
Pages (from-to)5028-5052
Number of pages25
JournalSIAM Journal on Control and Optimization
Volume48
Issue number8
DOIs
StatePublished - 2010

Keywords

  • Lyapunov functional
  • Second order evolution equations
  • Stabilization
  • Time-varying delay
  • Wave equations

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