Characteristic Boundary Layer Analysis Of A Class Of Quasilinear Equations

In this paper,we mainly study the asymptotic limit of the solution of the initial boundary value problem for two-dimensional quasilinear equations.We assume that the boundary of the corresponding inviscid equation is characteristic,and study the relationship between the viscous solution and the inviscid one.The boundary layer is characteristic.We use the method of matched asymptotic expansions to discuss the approximate solution of viscous equation in different domains.By using the method of weighted energy estimates,we obtain the existence of solutions for Prandtl type boundary layer equations.In order to prove the stability of the boundary layer,the error between the approximate solution and the real solution of the viscous problem is estimated.Finally,we obtain the asymptotic equivalence between the solutions of the viscous equation and the inviscid one.