关于非线性狄立克雷问题的一致有效渐近解

本文研究最高阶导数项带小参数的二阶拟线性椭圆型方程的狄立克雷问题.在退化方程不存在奇点的情形下,当参数ε是充分小时,证明了解的存在性和唯一性,并在整个区域导出解的一致有效渐近近似式.

On the Uniformly Valid Asymptotic Solution of a Non-linear Dirichlet Problem

In this paper, Dirichlet problem for second order quasi-linear elliptic equation with a small parameter at highest derivatives is studied. In case the degenerate equation has no singular point, and parameter ε is sufficiently small, the existence and uniqueness of solution are proved The uniformly valid asymptotic approximation of solution is derived in the entire region.