Periodic homogenization of a pseudo-parabolic equation via a spatial-temporal decomposition

Arthur Vromans, Fons van de Ven, A. Muntean

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Abstract

Pseudo-parabolic equations have been used to model unsaturated
fluid flow in porous media. In this paper it is shown how a pseudo-parabolic
equation can be upscaled when using a spatio-temporal decomposition employed in the Peszy´nska-Showalter-Yi paper [8]. The spatial-temporal decomposition transforms the pseudo-parabolic equation into a system containing an elliptic partial differential equation and a temporal ordinary differential equation. To strengthen our argument, the pseudo-parabolic equation has been given advection/convection/drift terms. The upscaling is done with the technique of periodic homogenization via two-scale convergence. The wellposedness of the extended pseudo-parabolic equation is shown as well. Moreover, we argue that under certain conditions, a non-local-in-time term arises from the elimination of an unknown.
Translated title of the contributionPeriodieke homgoenizatie van een pseudoparabolische vergelijking via een spatiaal-temporele decompositie
Original languageEnglish
Title of host publicationProceedings of The 20th European Conference on Mathematics for Industry
EditorsI Farag ́o, F. Izs ́ak, P. Simon
PublisherSpringer
Number of pages6
Publication statusPublished - 15 Apr 2019
Event20th European Conference on Mathematics for Industry - Budapest, Hungary
Duration: 18 Jun 201822 Jun 2018

Publication series

NameThe European Consortium for Mathematics in Industry Series

Conference

Conference20th European Conference on Mathematics for Industry
CountryHungary
CityBudapest
Period18/06/1822/06/18

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    Vromans, A., van de Ven, F., & Muntean, A. (2019). Periodic homogenization of a pseudo-parabolic equation via a spatial-temporal decomposition. In I. Farag ́o, F. Izs ́ak, & P. Simon (Eds.), Proceedings of The 20th European Conference on Mathematics for Industry (The European Consortium for Mathematics in Industry Series). Springer.