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

Abstract

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] $[0,1]$. 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 $L^{2} $-global exponential stability of the solution is shown. Numerical simulations are given to illustrate the efficiency of the developed control schemes.

Keywords

• Modified generalized Korteweg–de Vries–Burgers equation
• Exponential stability
• Boundary control