The Viscosity Vanishing Limit Of The Initial Boundary Value Problem For Two-Dimensional Parabolic Equations

This paper is concerned with the asymptotic limiting behavior of the solution to the two-dimensional quasi-linear scalar viscous equation with a weak boundary layer and an compressible strong boundary layer.It is proved that the boundary layers are nonlinearly stable for viscous conservation laws with grueling-nonlinear fluxes.This article is organized as follows.The first chapter describes the question,gives the equation model and the main conclusions.In the second chapter,using the matching asymptotic analysis method constructs the approximate solution.The third Chapter,using basic energy estimates gets the stability analysis.