| 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
eugene.f.kramer@uc.edu
2
Department of Mathematical Sciences, University of
Cincinnati, Cincinnati, 45221
Ohio,
USA
rivasie@mail.uc.edu; zhangb@ucmail.uc.edu
3
IMPA, Estrada
Dona Castorina 110, 22460-320
Rio de Janeiro,
Brasil.
Received:
27
March
2012
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
© EDP Sciences, SMAI, 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.