On the boundary control of a parabolic system coupling KS-KdV and Heat equations

Abstract

This paper presents a control problem for a one-dimensional nonlinear parabolic system. The system consists of a Kuramoto-Sivashinsky-Korteweg de Vries equation coupled to a heat equation. The problem of boundary controllability is discussed. The local null-controllability of the system is proven. The proof is based on a Carleman estimates approach to deal with the linearized system around the origin. A local inversion theorem is applied to get the result for the nonlinear system.