Viscous Vanishing Limits For Nonlinear Systems Of Equations In Multilayer Structures

In this thesis,we study the vanishing viscous limit of one-dimensional nonlinear viscous system with multi-layer structure.It is proved that when two non-interacting shock waves satisfy the entropy condition for the inviscid system,the asymptotic equivalence can be achieved between the solution of the viscous system and the solution of the inviscid system.This is proved based on matched asymptotic analysis and energy estimate related to the stability theory of viscous shock profile.First,the approximate solution of the viscosity system is constructed by the multi-scale matched asymptotic expansion method,and then the final conclusion is obtained by the stability analysis with the method of energy estimate.