Exact controllability of a nonlinear korteweg de vries equation on a critical spatial domain

摘要

We consider the boundary controllability problem for a nonlinear Korteweg - de Vries equation with the Dirichlet boundary condition. We study this problem for a spatial domain with a critical length for which the linearized control system is not controllable. In order to deal with the nonlinearity, we use a power series expansion of second order. We prove that the nonlinear term gives the local exact controllability around the origin provided that the time of control is large enough.