Consider a strictly hyperbolic n x n system of conservation laws in one space dimension:
ut+f(u)x=0.
Assuming that the initial data has small total variation, the global existence of weak solutions was proved by Glimm [9], while the uniqueness and stability of entropy admissible BV solutions was recently established in a series of papers [2 4 5 6 7 13]. See also [3] for a comprehensive presentation of these results. A long standing open question is whether these discontinuous solutions can be obtained as vanishing viscosity limits. More precisely, given a smooth initial data u ̄:R↦Rn with small total variation, consider the parabolic Cauchy problem
ut+A(u)ux=εuxx,
u(0,x)=u ̄(x).
