A two-scale reaction-diffusion system: Homogenization and fast-reaction limits

S.A. Meier, A. Muntean

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Abstract

We investigate a reaction-diffusion process in a two-phase layered material with relevant microscopic length scale e. In one phase, we assume di??usion-like macroscopic transport, while in the second phase, a fast chemical reaction with reaction constant k dominates the slow molecular di??usion (of order of O(e2)). The fast reaction mechanism causes spatial segregation of the reactants within the microstructure. First the homogenization limit e ¿ 0 is taken, which leads to a two-scale model. Afterwards, we pass to the fast-reaction limit k ¿ 8 and obtain a two-scale reaction-diffusion system with a moving boundary traveling within the microstructure. We show positivity, L8-estimates, uniqueness, and global existence of weak solutions to all reaction-diffusion systems discussed here.
Original languageEnglish
Title of host publicationCurrent Advances in Nonlinear Analysis and Related Topics
Place of PublicationTokyo
PublisherGakkotosho
Pages441-459
Publication statusPublished - 2010

Publication series

NameGakuto International Series, Mathematical Sciences and Applications
Volume32

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