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

Published online by Cambridge University Press:  10 January 2013

Eugene Kramer ,
Ivonne Rivas  and
Bing-Yu Zhang
Eugene Kramer
Affiliation:
Department of Mathematics, Physics, and Computer Science, Raymond Walters College, University of Cincinnati, Cincinnati, 45236 Ohio, USA. eugene.f.kramer@uc.edu
Ivonne Rivas
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, 45221 Ohio, USA; rivasie@mail.uc.edu; zhangb@ucmail.uc.edu IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brasil.
Bing-Yu Zhang
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, 45221 Ohio, USA; rivasie@mail.uc.edu; zhangb@ucmail.uc.edu
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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 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].

Keywords

The Kortweg-de Vries equationwell-posednessnon-homogeneous boundary value problem
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 2 , April 2013 , pp. 358 - 384
Copyright
© EDP Sciences, SMAI, 2013

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