Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
Walid Ben Youssef; Thierry Colin
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 34, Issue: 4, page 873-911
- ISSN: 0764-583X
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topBen Youssef, Walid, and Colin, Thierry. "Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems." ESAIM: Mathematical Modelling and Numerical Analysis 34.4 (2010): 873-911. <http://eudml.org/doc/197564>.
@article{BenYoussef2010,
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.
},
author = {Ben Youssef, Walid, Colin, Thierry},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Hyperbolic systems; systems of KdV-type; Euler-Poisson; water-waves; asymptotic expansion;
long-wave approximation.; quasilinear symmetric hyperbolic systems; long wave limit; Euler equations; Euler-Poisson systems},
language = {eng},
month = {3},
number = {4},
pages = {873-911},
publisher = {EDP Sciences},
title = {Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems},
url = {http://eudml.org/doc/197564},
volume = {34},
year = {2010},
}
TY - JOUR
AU - Ben Youssef, Walid
AU - Colin, Thierry
TI - Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 4
SP - 873
EP - 911
AB -
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.
LA - eng
KW - Hyperbolic systems; systems of KdV-type; Euler-Poisson; water-waves; asymptotic expansion;
long-wave approximation.; quasilinear symmetric hyperbolic systems; long wave limit; Euler equations; Euler-Poisson systems
UR - http://eudml.org/doc/197564
ER -
References
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Citations in EuDML Documents
top- Stéphane Labbé, Lionel Paumond, Numerical comparisons of two long-wave limit models
- Stéphane Labbé, Lionel Paumond, Numerical comparisons of two long-wave limit models
- Fabrice Béthuel, Raphaël Danchin, Philippe Gravejat, Jean-Claude Saut, Didier Smets, Les équations d’Euler, des ondes et de Korteweg-de Vries comme limites asymptotiques de l’équation de Gross-Pitaevskii
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