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the kortweg-de vries equation

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Well-posedness of a class of non-homogeneous boundary valueproblems of the Korteweg-de Vries equation on a finite domain ∗∗∗
Eugene Kramer, Ivonne Rivas, Bing-Yu Zhang
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 19 / Issue 2 / April 2013

Published online by Cambridge University Press:

10 January 2013, pp. 358-384

Print publication:

April 2013
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In this paper, we study a class of Initial-Boundary Value Problems proposed by Colin andGhidaglia for the Korteweg-de Vries equation posed on a bounded domain(0,L). We show that this class of Initial-Boundary Value Problems islocally well-posed in the classical Sobolev spaceHs(0,L) for s > -3/4, which provides a positive answer to one of the openquestions of Colin and Ghidaglia [Adv. Differ. Equ. 6 (2001)1463–1492].