Boundary control of the generalized Korteweg-de Vries-Burgers equation

This paper considers the boundary control problem of the generalized Korteweg-de Vries-Burgers (GKdVB) equation on the interval [0, 1]. We derive a control law of the form u(0,t) = u(x)(1,t) =u(xx)(1,t) + 1/mu(alpha+1) (1,t) =0, where mu > 0 and alpha is a positive integer, and prove that it guarantees L-2-global exponential stability, H-1-global asymptotic stability, and H-1-semiglobal exponential stability. Numerical results supporting the analytical ones for both the controlled and uncontrolled equations are presented using a finite element method.