Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain

Abstract

In this paper, we study a class of Initial-Boundary Value Problems proposed by Colin and Ghidaglia for the Korteweg-de Vries equation posed on a bounded domain (0,L). We show that this class of Initial-Boundary Value Problems is locally well-posed in the classical Sobolev space H s (0,L) for s> � 3 , which provides a positive answer to one of the open questions of Colin and Ghidaglia (Adv.