Claudia Timofte
University of Bucharest, Bucharest, Romania

In this talk, we shall present some homogenization results for a class of non-local problems in a two-phase composite material made up of a hosting medium in which a periodic array of perfect heat conductors is inserted. The temperature in the hosting medium is governed by a standard heat equation, while, inside each inclusion, the temperature depends only on time and satisfies a non-standard ordinary differential equation, involving a non-local condition. Across the interface between the two conductive regions, the thermal potentials of the two phases are coupled through an imperfect transmission condition. By using periodic homogenization techniques, several macroscopic models are obtained at the limit, depending on the magnitude of the interfacial heat exchange ([1-2]). Joint work with Micol Amar and Daniele Andreucci.

[1] M. Amar, D. Andreucci, C. Timofte, Heat conduction in composite media involving imperfect contact and perfectly conductive inclusions, Mathematical Methods in the Applied Sciences, 45 (17), 11355-11379, 2022
[2] M. Amar, D. Andreucci, C. Timofte, Asymptotic analysis for non-local problems in composites with different imperfect contact conditions, Applicable Analysis, 2022, DOI: 10.1080/00036811.2022.2120867.