We are concerned with a strictly hyperbolic system of conservation laws , where runs in a region of , 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 and show, under some more or less technical assumptions, that the approximate solutions given either by the vanishing viscosity method or by the Godunov scheme converge to weak entropy solutions as 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 .
Cite this article
Sylvie Benzoni-Gavage, Denis Serre, Compacité par compensation pour une classe de systèmes hyperboliques de lois de conservation. Rev. Mat. Iberoam. 10 (1994), no. 3, pp. 557–579DOI 10.4171/RMI/161