Local rapid stabilization for a Korteweg-de Vries equation with a Neumann boundary control on the right

Jean-Michel Coron, Qi Lü

Published 2013-11-16, updated 2014-03-19Version 2

This paper is devoted to the study of the rapid exponential stabilization problem for a controlled Korteweg-de Vries equation on a bounded interval with homogeneous Dirichlet boundary conditions and Neumann boundary control at the right endpoint of the interval. For every noncritical length, we build a feedback control law to force the solution of the closed-loop system to decay exponentially to zero with arbitrarily prescribed decay rates, provided that the initial datum is small enough. Our approach relies on the construction of a suitable integral transform.