@inbook{8e665d0518d849a38f1c49307f94921d,

title = "A two-scale reaction-diffusion system: Homogenization and fast-reaction limits",

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.",

author = "S.A. Meier and A. Muntean",

year = "2010",

language = "English",

series = "Gakuto International Series, Mathematical Sciences and Applications",

publisher = "Gakkotosho",

pages = "441--459",

booktitle = "Current Advances in Nonlinear Analysis and Related Topics",

}