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.
N1 - Publisher Copyright:
© 2019, The Author(s).
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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U2 - 10.1186/s13662-019-2376-x
DO - 10.1186/s13662-019-2376-x
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 -