| Issue |
ESAIM: COCV
Volume 19, Number 2, April-June 2013
|
|
|---|---|---|
| Page(s) | 358 - 384 | |
| DOI | https://doi.org/10.1051/cocv/2012012 | |
| Published online | 10 January 2013 | |
Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain∗,∗∗
1
Department of Mathematics, Physics, and Computer Science, Raymond
Walters College, University of Cincinnati, Cincinnati, 45236
Ohio,
USA
This email address is being protected from spambots. You need JavaScript enabled to view it.
2
Department of Mathematical Sciences, University of
Cincinnati, Cincinnati, 45221
Ohio,
USA
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; This email address is being protected from spambots. You need JavaScript enabled to view it.
3
IMPA, Estrada
Dona Castorina 110, 22460-320
Rio de Janeiro,
Brasil.
Received:
27
March
2012
Revised:
18
November
2011
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].
Mathematics Subject Classification: 35Q53
Key words: The Kortweg-de Vries equation / well-posedness / non-homogeneous boundary value problem
The authors would like to thank the referees for their comments and suggestions which have significantly improved the quality of the paper.
This work was partially supported by a Grant from the Simons Foundation (#201615 to Bingyu Zhang).
© EDP Sciences, SMAI, 2013
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