Vanishing viscosity limit for a one-dimensional viscous conservation law in the presence of two noninteracting shocks

In this article, we study the inviscid limit of the solution to the Cauchy problem of a one-dimensional viscous conservation law, where the second-order term is nonlinear. Under the assumption that the inviscid equation admits a piecewise smooth solution with two noninteracting entropy shocks, we prove that the solution of the viscous equation converges uniformly to the piecewise smooth inviscid solution away from the shocks, even the strength of shocks is not small.