Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Correctors for the Neumann problem in thin domains with locally periodic oscillatory structure


Authors: Marcone C. Pereira and Ricardo P. Silva
Journal: Quart. Appl. Math. 73 (2015), 537-552
MSC (2010): Primary 35B25, 35B27, 74Kxx
DOI: https://doi.org/10.1090/qam/1388
Published electronically: June 12, 2015
MathSciNet review: 3400758
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Abstract: In this paper we are concerned with convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain exhibiting highly oscillatory behavior in part of its boundary. We deal with the resonant case in which the height, amplitude and period of the oscillations are all of the same order, which is given by a small parameter $ \epsilon > 0$. Applying an appropriate corrector approach we get strong convergence when we replace the original solutions by a kind of first-order expansion through the Multiple-Scale Method.


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Additional Information

Marcone C. Pereira
Affiliation: Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, São Paulo SP, Brazil
Email: marcone@usp.br

Ricardo P. Silva
Affiliation: Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, Rio Claro SP, Brazil
Email: rpsilva@rc.unesp.br

DOI: https://doi.org/10.1090/qam/1388
Keywords: Thin domains, correctors, boundary oscillation, homogenization.
Received by editor(s): October 10, 2013
Published electronically: June 12, 2015
Additional Notes: The first author was partially supported by CNPq 305210/2008-4 and FAPESP 2008/53094-4 and 2010/18790-0, Brazil
The second author was partially supported by FUNDUNESP 0135812 and FAPESP 2008/53094-4 and 2012/06753-8, Brazil
Article copyright: © Copyright 2015 Brown University

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