Discussion on: ''Adaptive Boundary Control of the Forced Generalized Korteweg-de Vries-Burgers Equation''

This paper considers the adaptive control problem of the forced generalized Korteweg-de Vries-Burgers (GKdVB) equation when the spatial domain is [0,1]. Three different adaptive control laws are designed for the forced GKdVB equation when either the kinematic viscosity or the dynamic viscosity is unknown, or when both viscosities and are unknowns. The L -global exponential stability of the solutions of these equations is shown for each of the proposed control laws by using the Lyapunov theory. Numerical simulations based on the Finite Element method (FEM) are presented to validate the analytical developments.