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

N. Smaoui; B. Chentouf; A. Alalabi

doi:10.1186/s13662-019-2376-x

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 journal › Article › peer-review

9 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 language	English
Article number	449
Journal	Advances in Difference Equations
Volume	2019
Issue number	1
DOIs	https://doi.org/10.1186/s13662-019-2376-x
Publication status	Published - Dec 1 2019
Externally published	Yes

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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10.1186/s13662-019-2376-x

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title = "Modelling and nonlinear boundary stabilization of the modified generalized Korteweg–de Vries–Burgers equation",

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.",

keywords = "Boundary control, Exponential stability, Modified generalized Korteweg–de Vries–Burgers equation",

author = "N. Smaoui and B. Chentouf and A. Alalabi",

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doi = "10.1186/s13662-019-2376-x",

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TY - JOUR

T1 - Modelling and nonlinear boundary stabilization of the modified generalized Korteweg–de Vries–Burgers equation

AU - Smaoui, N.

AU - Chentouf, B.

AU - Alalabi, A.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

KW - Boundary control

KW - Exponential stability

KW - Modified generalized Korteweg–de Vries–Burgers equation

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M3 - Article

AN - SCOPUS:85074131761

SN - 1687-1839

VL - 2019

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 449

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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