Hyperbolic systems of balance laws via vanishing viscosity

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 uɛ, that are globally defined solutions to , satisfy uniform BV bounds exponentially decaying in time. Furthermore, they are stable in L1 with respect to the initial data. Finally, as ɛ→0, uɛ converges in to the admissible weak solution u of the system of balance laws ut+(f(u))x+g(u)=0 when A=Df.