A nonlinear boundary control for the dynamics of the generalized Korteweg-de Vries-Burgers equation

This paper considers the nonlinear boundary control problem of the Generalized Korteweg-de Vrie-Burgers (GKdVB) equation: ut = vuxx - µuxxx - u^αux, x ε [0,1], t 0. Different control laws were derived for different values of a (i.e., when a is an even positive integer, and when a is an odd positive integer) to show that the dynamics of the GKdVB equation is globally exponentially stable in L^2(0,1), and globally asymptotically stable and semi-globally exponentially stable in H^1 (0,1). Numerical results using the finite element method are presented to support the analytical results.