On a micro-macro system arising in diffusion-reaction problems in porous media
Sebastian A. Meier, Michael Böhm · Czech digital mathematics library · 2007
Abstract. In this note we describe a model of a reaction-diffusion process in a heterogeneous medium. The model resolves processes on the macro-scale as well as on the micro-scale by imposing a continuous family of local cell problems at each point of the medium. We list the model equations and derive a variational formulation in terms of special Sobolev spaces, constructed as direct integrals of Hilbert spaces. This construction modifies the concept of distributed-microstructure models of single-phase flow in fissured media, presented by Showalter et al. [1, 2]. The basic results on existence and uniqueness of weak solutions are given, and their proofs are sketched.