Upscaling of a diffusion problem with interfacial flux jump leading to a modified Barenblatt model
Renata Bunoiu, Claudia Timofte · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2018
Abstract In this paper, we study the homogenization of a diffusion problem in a highly heterogeneous composite medium formed by two constituents separated by an imperfect interface, where both the temperature and the flux exhibit jumps. The presence of the flux jump leads to a modified stationary Barenblatt model. Besides, we discuss two different geometrical settings, providing a mathematical justification for a physical phenomenon which is explained by the connectivity properties of the constituents.