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In this paper, we study a class of initial-boundary value problems for theKorteweg-de Vries equation posed on a bounded domain $(0,L)$. We show that theinitial-boundary value problem is locally well-posed in the classical Sobolevspace $H^s(0,L)$ for $s>-\frac34$, which provides a positive answer to one ofthe open questions of Colin and Ghidalia .

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