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Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems

Published online by Cambridge University Press:  15 April 2002

Walid Ben Youssef
Affiliation:
Mathématiques Appliquées de Bordeaux, Université Bordeaux 1 et CNRS UMR 5466, 351 Cours de la Libération, 33405 Talence Cedex, France. (benyou@math.u-bordeaux.fr)
Thierry Colin
Affiliation:
Mathématiques Appliquées de Bordeaux, Université Bordeaux 1 et CNRS UMR 5466, 351 Cours de la Libération, 33405 Talence Cedex, France. (colin@math.u-bordeaux.fr)
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Abstract

In this paper, we study the long wave approximation for quasilinear symmetric hyperbolic systems. Using the technics developed by Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that under suitable assumptions the long wave limit is described by KdV-type systems. The error estimate if the system is coupled appears to be better. We apply formally our technics to Euler equations with free surface and Euler-Poisson systems. This leads to new systems of KdV-type.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2000

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References

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Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
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