Global existence and uniqueness of solutions for a two-scale reaction–diffusion system with evolving pore geometry

We prove existence and uniqueness of weak solutions for a quasilinear parabolic system of two PDEs and one ODE that are coupled in a non-standard way. The problem results from the transformation of a two-scale model for reaction and diffusion in a time-dependent porous medium, where the evolution of the geometry is not a priori known but is coupled to the reaction–diffusion process itself. The analysis is based on a comparison principle for the two-scale problem and on the construction of a compact fixed-point operator.