The steepest point of the boundary layers of singularly perturbed semilinear elliptic problems
The steepest point of the boundary layers of singularly perturbed semilinear elliptic problems
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DOI：
10.1090/s0002-9947-04-03468-3
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发表时间：
2004-01
影响因子：
1.3
通讯作者：
T. Shibata
中科院分区：
文献类型：
--
作者：
T. Shibata
考虑非线性奇摄动问题-e2 Δu = f（u），u > 0 in Ω，u = 0 on Ω，其中Ω CRN（N > 2）是一个适当光滑的有界区域，e > 0是一个小参数.在f满足一定条件下，当e → 0时，对应于e的解u e产生边界层。通过建立具有精确第二项的边界层斜率的渐近公式，确定了边界层的最陡点。
We consider the nonlinear singularly perturbed problem -e 2 Δu = f(u), u > 0 in Ω, u = 0 on ∂Ω, where Ω C R N (N > 2) is an appropriately smooth bounded domain and e > 0 is a small parameter. It is known that under some conditions on f, the solution u e corresponding to e develops boundary layers when e → 0. We determine the steepest point of the boundary layers on the boundary by establishing an asymptotic formula for the slope of the boundary layers with exact second term.