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

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.

 Autoría: Gómez D., Lobo M., Pérez-Martínez M.,

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

Editorial: John Wiley & Sons

 Fecha de publicación: 01/10/2018

Nº de páginas: 10

Tipo de publicación: Artículo de Revista

 DOI: 10.1002/mma.5323

ISSN: 0170-4214,1099-1476

Proyecto español: MTM2013-44883-P

Url de la publicación: https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5323