Well-posedness and exponential stability of an abstract evolution equation with infinite memory and time delay

Aissa Guesmia*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

65 Scopus citations

Abstract

In this paper, we consider a second-order abstract linear equation with infinite memory and time delay terms. Under appropriate assumptions on the convolution kernel and on the weight of the delay, we prove the well-posedness and the exponential stability of the system. Our stability estimate proves that the unique dissipation given by the memory term is strong enough to stabilize exponentially the system in presence of delay. Some applications are also given.

Original languageEnglish
Pages (from-to)507-526
Number of pages20
JournalIMA Journal of Mathematical Control and Information
Volume30
Issue number4
DOIs
StatePublished - Dec 2013

Keywords

  • asymptotic behaviour
  • delay
  • memory
  • semigroups
  • well-posedness

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Well-posedness and exponential stability of an abstract evolution equation with infinite memory and time delay'. Together they form a unique fingerprint.

Cite this