Well-posedness and exponential stability of the Kawahara equation with a time-delayed localized damping

Boumediène Chentouf*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The aim of this article is to investigate the well-posedness and stability problems of the so-called Kawahara equation under the presence of an interior localized delayed damping. The system is shown to be well-posed. Furthermore, we prove that the trivial solution is exponentially stable in spite of the delay effect. Specifically, local and semi-global stability results are established according to the properties of the spatial distribution of the delay term.

Original languageEnglish
JournalMathematical Methods in the Applied Sciences
DOIs
Publication statusAccepted/In press - 2022
Externally publishedYes

Keywords

  • exponential stability
  • localized damping
  • nonlinear Kawahara equation
  • time-delay

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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