Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equation

Nejib Smaoui*, Boumediène Chentouf, Ala Alalabi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

The linear stabilization problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) is considered when the spatial variable lies in [0 , 1]. First, the existence and uniqueness of global solutions are proved. Next, the exponential stability of the equation is established in L2(0 , 1). Then, a linear adaptive boundary control is put forward. Finally, numerical simulations for both non-adaptive and adaptive problems are provided to illustrate the analytical outcomes.

Original languageEnglish
Article number457
JournalAdvances in Difference Equations
Volume2019
Issue number1
DOIs
Publication statusPublished - Dec 1 2019
Externally publishedYes

Keywords

  • Boundary control
  • Exponential stability
  • Modified generalized Korteweg–de Vries–Burgers equation
  • Well-posedness

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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