Boundary homogenization in perforated domains for adsorption problems with an advection term

We consider a model for the spreading of a substance through an incompressible fluid in a perforated domain , with . The fluid flows in a domain containing a periodical set of perforations ( ) placed along an inner surface . The size of the perforations is much smaller than the size of the character...

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Bibliographic Details
Published in:Applicable analysis 2016-07, Vol.95 (7), p.1517-1533
Main Authors: Brillard, A., Gómez, D., Lobo, M., Pérez, E., Shaposhnikova, T. A.
Format: Article
Language:English
Subjects:
Adsorption
Analysis of PDEs
Boundaries
Boundary homogenization
Homogenization
Homogenizing
Mathematical models
Mathematics
Nonlinearity
Partial differential equations
Perforations
porous media
Stokes problem
Surface chemistry
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Summary:We consider a model for the spreading of a substance through an incompressible fluid in a perforated domain , with . The fluid flows in a domain containing a periodical set of perforations ( ) placed along an inner surface . The size of the perforations is much smaller than the size of the characteristic period . An adsorption phenomena can occur on the boundaries of the perforations, where we assume a strongly nonlinear adsorption law with a large adsorption parameter. An advection term appears in the partial differential equation. We obtain the homogenized model which also involves a nonlinear transmission condition for the normal derivative on . The 'strange term' arising in this transmission condition is a nonlinear function implicitly defined by a functional equation. We deal with critical relations both for the size of perforations and the adsorption parameter while we use the energy method for variational inequalities to show the convergence.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2016.1153631