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We study the viscous limit problem for a general system of conservation laws. We prove that if the solution of the underlying inviscid problem is piecewise smooth with finitely many noninteracting shocks satisfying the entropy condition, then there exist solutions to the corresponding viscous system which converge to the inviscid solutions away from shock discontinuities at a rate of 1 as the viscosity coefficient  vanishes.

The Inviscid Limits to Piecewise Smooth Solutions for a General Parabolic System