区域外层具有奇性的Stiff问题的渐近分析

Asymptotical analysis of the Stiff problem with Singularity on the exterior domain

将区域外层具有奇性的Stiff问题(A)化为泛函的变分问题(B),然后利用Lions引入的渐近展开式讨论(B)的解,即设(B)的解是ε的冪级数展开式:u_ε=ε/u^(-1)+u^0+εu^1+ε~2u^2+…将u_ε代入(B)后求得系数u^(-1),u^0,u^1,u^2,…的一系列循环公式。

In this paper the Stiff problem (A) with Singularity on the exterior domain is reduced to the functional Variational problem(B).Using an asymptotical expansion introduced by Lions, we then discuss the Solution of (B), i.e., letting the solution of (B) be a power series expansion in ε:uε= u-1/ε +u0+εu1+ε2u2+… and Substituting uε into (B) , is obtoined a sequence of cyclic formulas of coefficients u-1, u0, u1, u2, ….