A nonlinear elliptic problem with terms concentrating in the boundary

A nonlinear elliptic problem with terms concentrating in the boundary

Author Aragao, Gleiciane S. Autor UNIFESP Google Scholar
Pereira, Antonio L. Google Scholar
Pereira, Marcone C. Google Scholar
Institution Universidade de São Paulo (USP)
Universidade Federal de São Paulo (UNIFESP)
Abstract In this paper, we investigate the behavior of a family of steady-state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a e-neighborhood of a portion G of the boundary. We assume that this e-neighborhood shrinks to G as the small parameter e goes to zero. Also, we suppose the upper boundary of this e-strip presents a highly oscillatory behavior. Our main goal here was to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on G, which depends on the oscillating neighborhood. Copyright (C) 2012 John Wiley & Sons, Ltd.
Keywords semilinear elliptic equations
nonlinear boundary value problems
singular elliptic equations
upper semicontinuity
concentrating terms
oscillatory behavior
Language English
Date 2012-06-01
Published in Mathematical Methods in the Applied Sciences. Hoboken: Wiley-Blackwell, v. 35, n. 9, p. 1110-1116, 2012.
ISSN 0170-4214 (Sherpa/Romeo, impact factor)
Publisher Wiley-Blackwell
Extent 1110-1116
Origin http://dx.doi.org/10.1002/mma.2525
Access rights Closed access
Type Article
Web of Science ID WOS:000304524900010
URI http://repositorio.unifesp.br/handle/11600/34933

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