Modelling and nonlinear boundary stabilization of the modified generalized Korteweg–de Vries–Burgers equation

N. Smaoui*, B. Chentouf, A. Alalabi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

In this paper, we study the modelling and nonlinear boundary stabilization problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) when the spatial domain is [0 , 1]. First, the MGKdVB equation is derived using the long-wave approximation and perturbation method. Then, two nonlinear boundary controllers are proposed for this equation and the L2-global exponential stability of the solution is shown. Numerical simulations are given to illustrate the efficiency of the developed control schemes.

Original languageEnglish
Article number449
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

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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