Asymptotics for models of non-stationary diffusion in domains with a surface distribution of obstacles

Gómez Gandarillas, Delfina; Lobo Hidalgo, Miguel; Pérez Martínez, María Eugenia

doi:10.1002/mma.5323

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Identificadores

URI: http://hdl.handle.net/10902/18165

DOI: 10.1002/mma.5323

ISSN: 0170-4214

ISSN: 1099-1476

Fecha

2019-01-15

Derechos

© John Wiley & Sons "This is the peer reviewed version of the following article: Gómez, D, Lobo, M, Pérez, ME. Asymptotics for models of non-stationary diffusion in domains with a surface distribution of obstacles. Math Meth Appl Sci. 2019; 42: 403? 413., which has been published in final form at [https://doi.org/10.1002/mma.5323]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."

Publicado en

Mathematical Methods in the Applied Sciences - Volume42, Issue1 15 January 2019. Pages 403-413

Editorial

John Wiley & Sons

Enlace a la publicación

https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5323

Palabras clave

Asymptotic expansions

Boundary homogenization

Critical parameters

Evolution problems

Nonlinear problems

Resumen/Abstract

We consider a time-dependent model for the diffusion of a substance through an incompressible fluid in a perforated domain ??, urn:x-wiley:mma:media:mma5323:mma5323-math-0001 with n?=?3,4. The fluid flows in a domain containing a periodical set of ?obstacles? (?\??) placed along an inner (n???1)?dimensional manifold urn:x-wiley:mma:media:mma5323:mma5323-math-0002. The size of the obstacles is much smaller than the size of the characteristic period ?. An advection term appears in the partial differential equation linking the fluid velocity with the concentration, while we assume a nonlinear adsorption law on the boundary of the obstacles. This law involves a monotone nonlinear function ? of the concentration and a large adsorption parameter. The ?critical adsorption parameter? depends on the size of the obstacles , and, for different sizes, we derive the time?dependent homogenized models. These models contain a ?strange term? in the transmission conditions on ?, which is a nonlinear function and inherits the properties of ?. The case in which the fluid velocity and the concentration do not interact is also considered for n???3.