Resumen de Compacité par compensation pour une classe de systèmes hyperboliques de p[mayor ó igual a]3 lois de conservation

Sylvie Benzoni-Gavage, D. Serre

• We are concerned with a strictly hyperbolic system of conservation laws ut + f(u)x = 0, where u runs in a region O 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 (ue)e>0 given either by the vanishing viscosity method or by the Godunov scheme converge to weak entropy solutions as e 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.