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

Abstract

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] $[0,1]$. First, the existence and uniqueness of global solutions are proved. Next, the exponential stability of the equation is established in L2(0,1) $L^{2} (0,1)$. 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

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