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

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.