Effective transmission conditions for reaction-diffusion processes in domains separated by thin channels - Bhattacharya, Apratim; Gahn, Markus; Neuss-Radu, Maria (Applicable Analysis, 2020)
We consider a reaction–diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order ϵ, and the equation inside the layer depends on the parameter ϵ and an additional parameter γ∈[−1,1), which describes the size of the diffusion in the layer. We derive effective models for the limit ϵ→0, when the channel-domain is replaced by an interface between the two bulk-domains.
Keywords: Array of channels; homogenization; two-scaleconvergence; reaction–diffusion equation; effective transmission conditions

Homogenization of a nonlinear drift-diffusion system for multiple charged species in a porous medium - Bhattacharya, Apratim; Gahn, Markus; Neuss-Radu, Maria (Nonlinear Analysis-Real World Applications, 2022)
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's equation for the electric potential. The diffusion terms depend nonlinearly on the concentrations. We consider non-homogeneous Neumann boundary condition for the electric potential. The aim is the rigorous derivation of an effective (homogenized) model in the limit when the scale parameter epsilon tends to zero. This is based on uniform a priori estimates for the solutions of the microscopic model. The crucial result is the uniform L-infinity-estimate for the concentration in space and time. This result exploits the fact that the system admits a nonnegative energy functional which decreases in time along the solutions of the system. By using weak and strong (two-scale) convergence properties of the microscopic solutions, effective models are derived in the limit epsilon -> 0 for different scalings of the microscopic model. (C) 2022 Elsevier Ltd. All rights reserved.
CRIS-Team WoS Importer:2022-07-15