Boundary feedback stabilization of the Korteweg–de Vries–Burgers equation posed on a finite interval

Abstract

This paper studies the boundary feedback stabilization problem of the Korteweg–de Vries–Burgers equation posed on a finite interval. A linear boundary feedback control law is proposed. Then the resulting closed-loop nonlinear system is shown not only to be globally well-posed, but also to be exponentially stable in the space Hs(0,ℓ) with s∈[0,3]. The sharp Kato smoothing property of the associated linear problem is revealed through the boundary integral operator, which plays a key role in our analysis.