JournalsrmiVol. 10, No. 3pp. 557–579

Compacité par compensation pour une classe de systèmes hyperboliques de p3p ≥ 3 lois de conservation

  • Sylvie Benzoni-Gavage

    Université Claude Bernard Lyon 1, Villeurbanne, France
  • Denis Serre

    École Normale Supérieure de Lyon, France
Compacité par compensation pour une classe de systèmes hyperboliques de $p ≥ 3$ lois de conservation cover
Download PDF

Abstract

We are concerned with a strictly hyperbolic system of conservation laws ut+f(u)x=0u_t + f( u)_x = 0, where uu runs in a region Ω\Omega of Rp\mathbb R^p, 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=3p = 3 and show, under some more or less technical assumptions, that the approximate solutions (uϵ)ϵ>0(u^\epsilon)_{\epsilon>0} given either by the vanishing viscosity method or by the Godunov scheme converge to weak entropy solutions as ϵ\epsilon 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>3p > 3.

Cite this article

Sylvie Benzoni-Gavage, Denis Serre, Compacité par compensation pour une classe de systèmes hyperboliques de p3p ≥ 3 lois de conservation. Rev. Mat. Iberoam. 10 (1994), no. 3, pp. 557–579

DOI 10.4171/RMI/161