极限方程有奇性的一类六阶椭圆型方程混合边值问题解的渐近式

Asymptotic Expansion of Solution of Mixed Boundary Value Problem for a Class Sixth Order Elliptic Equation when the Limit Equation Has Singularity

该文研究极限方程在部分边界上为退缩椭圆型(椭圆-抛物)的一类六阶椭圆型方程混合边值问题的奇摄动,在适当的假设下,应用改进了的多重尺度法,求得其解包括边界层和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.

In this paper, the author considered the singular perturbation of mixed boundaryvalue problem for a class sixth order elliptic equation when the limit equation is degenearatedelliptic equation (elliptic-parabolic) at the partial boundary. Under suitable assumptions, usingthe improving method of multiple scale, the uniformly valid asymptotic expansion of solutioninvolving boundary layer and cover layer of arbitrary order at the whole half-circle region is ob-tained except two corner point at the half-circle region.