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 for the Korteweg-de Vries equation posed on a bounded domain $(0,L)$. We show that the initial-boundary value problem is locally well-posed in the classical Sobolev space $H^s(0,L)$ for $s>-\frac{3}{4}$, which provides a positive answer to one of the open questions of Colin and Ghidalia .