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ANALYSIS OF BOUNDARY LAYER SINGULARITY
Author(s): ZHANG WEITAO
Pages: 87-
101
Year: 1984
Issue:
2
Journal: Journal of Systems Science and Mathematical Sciences
Keyword: 奇性; 边界层; identical; ANALY; entirely; 玩山; 尹石; exterior; hoose; 二甲;
Abstract: 设 λ∈[λ0,∞)(0<λ0<<1),H1=H02(Ω)∩H3(Ω),H2=H01(Ω)∩H3(Ω),H3=H3(Ω),k1=1/4,k2=1/12,k3=1/36,J6(λ)=integral d(x,Γ)≥aλlog(1+a-β |△▽(ue-u)|2dx,α(ε)=1/6×logε1/C(C>1).我们考虑问题(?)定理.若 u=f∈Hi,对问题(1),有如下三种情形成立:i)正规区域 当 λ0≤λ≤1/6-α(ε)时,有J6(λ)≤C‖f‖H3(Ω)2;ii)奇性增长区域当1/6-α(ε)<λ<1/6+ki/6时,有J6(λ)≤Cε-6λ+2ki‖f‖H3(Ω)2;iii)奇性稳定区域当 λ≥1/6+(ki)/6时,有J6(λ)≤Cε-1+ki‖f‖H3(Ω)2;其中 i=1,2,3,β≥(45)/(32),C 为同 ε 无关的常数(见图1).
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