Has A Viscable Viscosity Limit For Two Strongly Compressible Boundary Layers

In this paper, we study the limiting behavior of a clan of viscous equations as ε goes to zero.Here, we consider only non-characteristic boundary case. We first construct formally the threeterm approximate solutions by using the method of matched asymptotic expansions. Next, it is proved that the strong boundary layers are nonlinearly stable for viscous conservation laws with genuinely-nonlinear flux. The analysis for the results depends crucially on the structure of the underlying boundary layers. The proofs are based on basic energy estimates.