Viscous Vanishing Limit Under Multilayer Structure

In this paper,we study the asymptotic limit of the solution of one-dimensional non-linear viscous parabolic equation.The solution of the viscous equation converges uniformly to a piecewise smooth inviscid solution far from the shocks.We first construct the approxi-mate solution of the viscous equation by using the method of matched asymptotic analysis method,the aim is to understand the evolution and structure of the external inviscid hy-perbolic flow and shock layer solutions,then we give the detailed process of the proof of the stability by use the energy estimate,finally we establish asymptotic equivalence between the two kinds of equations.