Hyperbolic systems of balance laws via vanishing viscosity

Abstract

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 uε, that are globally defined solutions to utε + A (uε) uxε + g(uε) = εuxxε, satisfy uniform BV bounds exponentially decaying in time. Furthermore, they are stable in L1 with respect to the initial data. Finally, as ε → 0, uε converges in Lloc1 to the admissible weak solution u of the system of balance laws ut + (f (u))x + g (u) = 0 when A = Df. © 2005 Elsevier Inc. All rights reserved.