Advances in Differential Equations

On the dual Petrov-Galerkin formulation of the KdV equation on a finite interval

Olivier Goubet and Jie Shen

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Abstract

An abstract functional framework is developed for the dual Petrov-Galerkin formulation of the initial-boundary-value problems with a third-order spatial derivative. This framework is then applied to study the wellposedness and decay properties of the KdV equation in a finite interval.

Article information

Source
Adv. Differential Equations Volume 12, Number 2 (2007), 221-239.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867476

Mathematical Reviews number (MathSciNet)
MR2294504

Zentralblatt MATH identifier
1157.35093

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35A35: Theoretical approximation to solutions {For numerical analysis, see 65Mxx, 65Nxx} 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Citation

Goubet, Olivier; Shen, Jie. On the dual Petrov-Galerkin formulation of the KdV equation on a finite interval. Adv. Differential Equations 12 (2007), no. 2, 221--239. https://projecteuclid.org/euclid.ade/1355867476.


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Corrections

  • Correction: Olivier Goubet, Jie Shen. Corrigendum: "On the dual Petrov-Galerkin formulation of the KdV equation on a finite interval''. Adv. Differential Equations 13 (2008), no. 1-2, 199–200.