ON THE CONVERGENCE RATE OF VANISHING VISCOSITY APPROXIMATIONS FOR NONLINEAR HYPERBOLIC SYSTEMS

In this paper we study the vanishing viscosity limit of strictly hyperbolic systems, extending the earlier result in [A. Bressan and T. Yang, Comm. Pure Appl. Math., 57 ( 2004), pp. 1075-1109] to systems where each characteristic field can be either genuinely nonlinear or linearly degenerate. For a given initial data with small total variation, our main estimate shows that the L-1 distance between the exact solution u and a viscous approximation u(epsilon) is bounded by parallel to u(tau, .) - u(epsilon) (tau,.)parallel to(L1) = O(1) . (1 + tau)epsilon(1/4). Under the additional assumptions that the integral curves of all linearly degenerate fields are straight lines, we obtain the sharper estimate parallel to u(tau, .) - u(epsilon)(tau, .)parallel to(L1) = O(1) . (1 + tau)root epsilon vertical bar ln epsilon vertical bar.