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 L1 distance between the exact solution u and a viscous approximation ue is bounded by u(t, .) - u ^ε(t, .)L ¹ = O(1) . (1 + t)e1/4. Under the additional assumptions that the integral curves of all linearly degenerate fields are straight lines, we obtain the sharper estimate u(t, .) - u ^ε(t, .)L ¹ = O(1)(1 + t)ε| ln ε|.