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

Author:
T. Shibata

Translated by:

Journal:
Trans. Amer. Math. Soc. **356** (2004), 2123-2135

MSC (2000):
Primary 35J65, 35J60

DOI:
https://doi.org/10.1090/S0002-9947-04-03468-3

Published electronically:
January 6, 2004

MathSciNet review:
2031056

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the nonlinear singularly perturbed problem

where () is an appropriately smooth bounded domain and is a small parameter. It is known that under some conditions on , the solution corresponding to develops boundary layers when . 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.

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Additional Information

**T. Shibata**

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

Email:
shibata@mis.hiroshima-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-04-03468-3

Keywords:
Boundary layer,
singular perturbation,
semilinear elliptic equations

Received by editor(s):
October 3, 2002

Received by editor(s) in revised form:
July 11, 2003

Published electronically:
January 6, 2004

Article copyright:
© Copyright 2004
American Mathematical Society