Hyperbolic systems of balance laws via vanishing viscosity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:221

Article

Christoforou, CC

关键词: hyperbolic systems;    balance laws;    vanishing viscosity;    dissipative;   

DOI  :  10.1016/j.jde.2005.03.010

来源: Elsevier

【 摘 要 】

Global weak solutions of a strictly hyperbolic system of balance laws in one-space dimension are constructed by the vanishing viscosity method of Bianchini and Bressan. For global existence, a suitable dissipativeness assumption has to be made on the production term g. Under this hypothesis, the viscous approximations u(epsilon), that are globally defined solutions to u(t)(epsilon) +A(u(epsilon))u(x)(epsilon) + g(u(epsilon)) = epsilon u(xx)(epsilon), satisfy uniform BV bounds exponentially decaying in time. Furthermore, they are stable in L-1 with respect to the initial data. Finally, as epsilon -> 0, u(epsilon) converges in L-loc(1) to the admissible weak solution u of the system of balance laws u(t) + (f(u))(x) + g(u) = 0 when A = Df. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free