Well-posedness and stability results for the Korteweg–de Vries–Burgers and Kuramoto–Sivashinsky equations with infinite memory: A history approach

Boumediène Chentouf*, Aissa Guesmia

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The main concern of the present paper is to study the well-posedness and stability problem of two different dispersive systems subject to the effect of a distributed infinite memory term. The two systems are respectively governed by the one-dimensional Korteweg–de Vries–Burgers and Kuramoto–Sivashinsky equations in a bounded domain [0,1]. In order to deal with the presence of the memory term, we adopt the history approach. First, we show that both problems are well-posed in appropriate functional spaces by means of the Fixed-Point Theorem provided that the initial condition is sufficiently small. Then, the energy method enables us to provide a decay estimate of the systems’ energy according to the assumptions satisfied by the physical parameters and the memory kernel.

Original languageEnglish
Article number103508
JournalNonlinear Analysis: Real World Applications
Publication statusPublished - Jun 2022
Externally publishedYes


  • Energy method
  • Infinite memory
  • Korteweg–de Vries–Burgers equation
  • Kuramoto–Sivashinsky equation
  • Stability
  • Well-posedness

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

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