Well-posedness and exponential stability results for a nonlinear Kuramoto-Sivashinsky equation with a boundary time-delay

Boumediène Chentouf*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

The main concern of this article is to deal with the presence of a boundary delay in the nonlinear Kuramoto-Sivashinsky equation. First, we prove that the whole system is well-posed under a smallness assumption on the initial data and a condition on the parameter involved in the delay term. Then, the solution is shown to decay exponentially despite the presence of the delay. These findings are proved by considering several situations depending on the physical parameters of the system.

Original languageEnglish
Article number144
JournalAnalysis and Mathematical Physics
Volume11
Issue number4
DOIs
Publication statusPublished - Dec 2021
Externally publishedYes

Keywords

  • Boundary delay
  • Exponential Stability
  • Nonlinear Kuramoto-Sivashinsky equation
  • Well-posedness

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics

Cite this