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 - 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 -