摘要
在区间I =[0 ,b]与球域Ω ={x∈RN,N〉 1:|x |〈b}上 ,对a〉 1,构造出奇异问题-△u =λua ,u〉 0 ,x∈Ω ,u| Ω=0的精细逼近解 .其中在区间上的逼近解为最佳 ,即当a =3时 ,精确解是u =[λb2 ]1a +1[x(b -x) ]2a +1;而在球域上的逼近解是几乎最优的 .这里λ〉 0为参数 .
The nice funcitions are constructed,in which u ∈ C 2(Ω)satisfying u ≤ in Ω,△ ≤f (),x ∈ Ω,| Ω = 0 and △u ≥ f( u),x ∈ Ω, u | Ω = 0. It shows that the unique solution u ∈ C 2(Ω) of the problem - △ u = λu a,u> 0,x ∈ Ω,u| Ω = 0 satisfying u ≤ u ≤ in Ω, where a > 1,λ> 0;Ω = or Ω is a ball. In the first case,the best approximation is obtained, i.e., if α =3,then the exact solution u = 1a+1 2a+1 ; and in the second case,the approximation is almost optimal.
出处
《烟台大学学报（自然科学与工程版）》
CAS
2002年第3期157-160,共4页
Journal of Yantai University(Natural Science and Engineering Edition)
基金
国家自然科学基金项目 (10 0 710 6 6 )
