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2001 An initial-boundary value problem for the Korteweg-de Vries equation posed on a finite interval
Thierry Colin, Jean-Michel Ghidaglia
Adv. Differential Equations 6(12): 1463-1492 (2001).

Abstract

The Korteweg--de Vries equation occurs as a model for unidirectional propagation of small amplitude long waves in numerous physical systems. The aim of this work is to propose a well-posed mixed initial--boundary value problem when the spacial domain is of finite extent. More precisely, we establish local existence of solutions for arbitrary initial data in the Sobolev space $H^1$ and global existence for small initial data in this space. In a second step we show global strong regularizing effects.

Citation

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Thierry Colin. Jean-Michel Ghidaglia. "An initial-boundary value problem for the Korteweg-de Vries equation posed on a finite interval." Adv. Differential Equations 6 (12) 1463 - 1492, 2001.

Information

Published: 2001
First available in Project Euclid: 2 January 2013

zbMATH: 1022.35055
MathSciNet: MR1858429

Subjects:
Primary: 35Q53
Secondary: 35A07

Rights: Copyright © 2001 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.6 • No. 12 • 2001
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