Rapid boundary stabilization of the Korteweg-de Vries equation on a bounded domain I: Well-posedness

In this project we are concerned with the rapid stabilization problem for a nonlinear control system described by the Korteweg-de Vries equation on a bounded domain. In understanding this problem, we need address a class of initial-boundary value problems for the Korteweg-de Vries equation which turns out to be interesting and challenging. In this note we mainly establish the local well-posedness, in the L²-based Sobolev spaces, of this class of initial-boundary value problems by a semigroup approach developed by Kato [1-4] and the Banach Contraction Mapping Principle.