Compensated compactness for a class of hyperbolic systems of p ≥ 3 conservation laws

Sylvie Benzoni-Gavage; Denis Serre

Revista Matemática Iberoamericana (1994)

  • Volume: 10, Issue: 3, page 557-579
  • ISSN: 0213-2230

Abstract

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We are concerned with a strictly hyperbolic system of conservation laws ut + f(u)x = 0, where u runs in a region Ω of Rp, such that two of the characteristic fields are genuinely non-linear whereas the other ones are of Blake Temple's type. We begin with the case p = 3 and show, under more or less technical assumptions, that the approximate solutions (uε)ε>0 given either by the vanishing viscosity method or by the Godunov scheme converge to weak entropy solutions as ε goes to 0. The first step consists in using techniques from the Blake Temple systems lying in the separate works of Leveque-Temple and Serre. Then we apply a compensated compactness method and the theory of Di Perna on 2 x 2 genuinely non-linear systems. Eventually the proof is extended to the general case p > 3.

How to cite

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Benzoni-Gavage, Sylvie, and Serre, Denis. "Compacité par compensation pour une classe de systèmes hyperboliques de p ≥ 3 lois de conservation.." Revista Matemática Iberoamericana 10.3 (1994): 557-579. <http://eudml.org/doc/39465>.

@article{Benzoni1994,
author = {Benzoni-Gavage, Sylvie, Serre, Denis},
journal = {Revista Matemática Iberoamericana},
keywords = {Corriente de fluidos; Flujos bifásicos; Problemas hiperbólicos; Gas de petróleo; Métodos fisicomatemáticos; vanishing viscosity method; compensated compactness; Temple type systems; pseudo-entropies; isothermal two-phase flow},
language = {fre},
number = {3},
pages = {557-579},
title = {Compacité par compensation pour une classe de systèmes hyperboliques de p ≥ 3 lois de conservation.},
url = {http://eudml.org/doc/39465},
volume = {10},
year = {1994},
}

TY - JOUR
AU - Benzoni-Gavage, Sylvie
AU - Serre, Denis
TI - Compacité par compensation pour une classe de systèmes hyperboliques de p ≥ 3 lois de conservation.
JO - Revista Matemática Iberoamericana
PY - 1994
VL - 10
IS - 3
SP - 557
EP - 579
LA - fre
KW - Corriente de fluidos; Flujos bifásicos; Problemas hiperbólicos; Gas de petróleo; Métodos fisicomatemáticos; vanishing viscosity method; compensated compactness; Temple type systems; pseudo-entropies; isothermal two-phase flow
UR - http://eudml.org/doc/39465
ER -

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