Null controllability of a linearized Korteweg-de Vries equation by backstepping approach

Shengquan Xiang (1)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

This paper deals with the controllability problem of a linearized Korteweg-de Vries equation on bounded interval. The system has a homogeneous Dirichlet boundary condition and a homogeneous Neumann boundary condition at the right end-points of the interval, a non homogeneous Dirichlet boundary condition at the left end-point which is the control. We prove the null controllability by using a backstepping approach, a method usually used to handle stabilization problems.

Mots clés: spectral theory; null controllability; Korteweg-de Vries; backstepping; stabilization

Domaines: Mathématiques [math]

Shengquan Xiang. Null controllability of a linearized Korteweg-de Vries equation by backstepping approach. 2017. ⟨hal-01468750v1⟩