A two‐scale reaction‐diffusion system with time‐dependent microstructure
Sebastian A. Meier, Michael Böhm · PAMM · 2006
Abstract We present a two‐scale model for reactive transport in a unsaturated porous medium. Reaction and diffusion of a gas dissolved in the pore water is modelled at the pore‐scale, while the fast transport of the gas in the air phase is described by an averaged equation. The pore geometry is allowed to vary in time to account for temporal changes of the domain occupied by the pore water. The resulting semilinear parabolic system of PDEs is coupled in a non‐standard way. After a transformation to a fixed domain, the existence of a unique weak W1,p ‐solution is established by semigroup methods. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)