Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain∗,∗∗
Department of Mathematics, Physics, and Computer Science, Raymond
Walters College, University of Cincinnati, Cincinnati, 45236
2 Department of Mathematical Sciences, University of Cincinnati, Cincinnati, 45221 Ohio, USA
3 IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brasil.
Revised: 18 November 2011
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 Hs(0,L) for s > -3/4, which provides a positive answer to one of the open questions of Colin and Ghidaglia [Adv. Differ. Equ. 6 (2001) 1463–1492].
Mathematics Subject Classification: 35Q53
Key words: The Kortweg-de Vries equation / well-posedness / non-homogeneous boundary value problem
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