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

Nejib Smaoui; Boumediène Chentouf; Ala Alalabi

doi:10.1186/s13662-019-2387-7

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 journal › Article › peer-review

6 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 language	English
Article number	457
Journal	Advances in Difference Equations
Volume	2019
Issue number	1
DOIs	https://doi.org/10.1186/s13662-019-2387-7
Publication status	Published - Dec 1 2019
Externally published	Yes

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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10.1186/s13662-019-2387-7

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title = "Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equation",

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.",

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

author = "Nejib Smaoui and Boumedi{\`e}ne Chentouf and Ala Alalabi",

note = "Publisher Copyright: {\textcopyright} 2019, The Author(s).",

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doi = "10.1186/s13662-019-2387-7",

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TY - JOUR

T1 - Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equation

AU - Smaoui, Nejib

AU - Chentouf, Boumediène

AU - Alalabi, Ala

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

KW - Boundary control

KW - Exponential stability

KW - Modified generalized Korteweg–de Vries–Burgers equation

KW - Well-posedness

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DO - 10.1186/s13662-019-2387-7

M3 - Article

AN - SCOPUS:85074324202

SN - 1687-1839

VL - 2019

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 457

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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