Stability of Burgers-Korteweg-de Vries Equation
For Burgers-Korteweg-de Vries(KdVB) equation defined on a finite spatial interval with unknown viscosity, a nonlinear boundary control law and an adaptation law are proposed. Based on Lyapunov direct method, the global asymptotic stability of the closed-loop system is proved. The stochastic case of Burgers-Korteweg-de Vries equation is also considered. The exponential stability of the delayed KdVB equation is also proved if the delay parameter is sufficiently small.