极限方程有奇性的一类高阶椭圆型方程边值问题的奇摄动

Singular Perturbation of Boundary Value Problem for Higher Order Elliptic Equation when the Limit Equation Has Singularity

研究极限方程在部分边界上为退缩椭圆型方程（椭圆——抛物）的一类高阶椭圆型方程边值问题的奇摄动．在适当的假设下，应用改进了的多重尺度法，求得其解包括套层在内除了半圆域的两个角点外，在整个半圆域中有任意阶的一致有效的渐近展开式．

The author considered the singular perturbation of boundary value problem for a higher order elliptic equation when the limit equation is degenerated elliptic equation(ellipticparabolic) at the partial boundary.Under the suitable assumptions,using the improving method of multiple scale,the uniformly valid asymptotic expansion of solution involving cover layer at the whole halfcircle region is obtained except two corner point at the halfcircle region.