Modelling and nonlinear boundary stabilization of the modified generalized Korteweg–de Vries–Burgers equation-Reference-Cited by-同舟云学术

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

Published:2019-10-25 Issue:1 Volume:2019 Page:
ISSN:1687-1847
Container-title:Advances in Difference Equations
language:en
Short-container-title:Adv Differ Equ

Author:

Smaoui N.,Chentouf B.,Alalabi A.

Abstract

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

$[0,1]$

[ 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

$L^{2} $

L 2 -global exponential stability of the solution is shown. Numerical simulations are given to illustrate the efficiency of the developed control schemes.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Link

http://link.springer.com/content/pdf/10.1186/s13662-019-2376-x.pdf

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