TY - JOUR
T1 - Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equation
AU - Smaoui, Nejib
AU - Chentouf, Boumediène
AU - Alalabi, Ala
N1 - Funding Information:
The authors would like to thank the College of Graduate Studies for supporting this research. The authors are also grateful to the editor and the two anonymous referees for their valuable suggestions and comments which have led to an improved version of this paper. Not applicable.
Publisher Copyright:
© 2019, The Author(s).
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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U2 - 10.1186/s13662-019-2387-7
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 -