Null Controllability of a Coupled System of Two Korteweg-de Vries Equations from the Left Dirichlet Boundary Conditions

Abstract

In this paper, we consider a coupled system of two Korteweg-de Vries equations on a bounded domain. We establish the null controllability of this system from the left Dirichlet boundary conditions. Combining the analysis of a linearized system and a fixed point argument, this controllability result is reduced to prove the null controllability of a linearized system with two distributed controls.