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arXiv · 1012.1057

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

Eugene Kramer·Ivonne Rivas·Bing-Yu Zhang
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Abstract

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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Eugene Kramer, Ivonne Rivas, Bing-Yu Zhang. 2010-12-06. Well-posedness of a Class of Non-homogeneous Boundary Value Problems of the Korteweg-de Vries Equation on a Finite Domain. https://arxiv.org/abs/1012.1057

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