Boundary layers for quasilinear parabolic equation (Q5942494)

Boundary value problems for quasilinear parabolic equations arise by studying propagation of sound with acoustic nonlinearity or by solving problems of nonlinear optics. The boundary value problem for a so-called model equation of gas dynamics is considered. It is found that there are two different circumstances of such a problem: 1) in spite of the fact that the solution of a degenerate boundary value problem is satisfying both the boundary, and the initial conditions the problem itself is singularly perturbed; 2) in the above mentioned case all equations defining functions of the boundary layers type are linear equations. Uniformly asymptotic, in relation to a small parameter, expansion for the solution of quasilinear elliptic equation is constructed.