The steepest point of the boundary layers of singularly perturbed semilinear elliptic problems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The steepest point of the boundary layers of singularly perturbed semilinear elliptic problems

Authors:	T Shibata

Institution:	The Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan

Abstract:	We consider the nonlinear singularly perturbed problem $\begin{displaymath}-\epsilon^2\Delta u = f(u), \enskip u > 0 \quad \mbox{in} \enskip \Omega, u = 0 \quad \mbox{on} \enskip \partial\Omega, \end{displaymath}$ where $\Omega \subset {\mathbf{R}}^N$ ( $N \ge 2$ ) is an appropriately smooth bounded domain and $\epsilon > 0$ is a small parameter. It is known that under some conditions on , the solution $u_\epsilon$ corresponding to $\epsilon$ develops boundary layers when $\epsilon \to 0$ . 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.

Keywords:	Boundary layer singular perturbation semilinear elliptic equations

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