Well-posedness of a Class of Non-homogeneous Boundary Value Problems of the Korteweg-de Vries Equation on a Finite Domain

Details Well-posedness of a Class of Non-homogeneous Boundary Value Problems of the Korteweg-de Vries Equation on a Finite Domain Well-posedness of a Class of Non-homogeneous Boundary Value Problems of the Korteweg-de Vries Equation on a Finite Domain

2010-12-06

arxiv.org/abs/1012.1057v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper, we study a class of initial-boundary value problems for the
Korteweg-de Vries equation posed on a bounded domain $(0,L)$. We show that the
initial-boundary value problem is locally well-posed in the classical Sobolev
space $H^s(0,L)$ for $s>-\frac34$, which provides a positive answer to one of
the open questions of Colin and Ghidalia .

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