Relaxations semi-linéaire et cinétique des systèmes de lois de conservation

✍ Scribed by Denis Serre

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 161 KB
• Volume: 17
• Category: Article
• ISSN: 0294-1449
• DOI: 10.1016/s0294-1449(99)00105-5

✦ Synopsis

DiPerna (1983)

proved the convergence of the approximate solutions given by the vanishing viscosity method, towards an entropy solution of the underlying hyperbolic system. He used two main assumptions: the existence of convex positively invariant domains (in the sense of K.N. Chuey et al. (1977)) and genuine nonlinearity. We prove below that, under the same assumptions together with the subcharacteristic condition, the approximate solutions given by the semilinear relaxation converge too. Actually, our result stands for a more general approximation, first introduced by R. Natalini (1998).