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Double layer concentration and homogenization for the heat diffusion in a composite material

Micol Amar, Afsheen Ayub and Roberto Gianni

Vol. 12 (2024), No. 1, 19–45
Abstract

We investigate the possibility of deriving “nonstandard” transmission conditions, across a sharp contact interface, for a heat equation (in its static, i.e., elliptic, counterpart), by means of a concentration approach performed on a composite “thick” interface separating two thermally conductive media. Subsequently, a homogenization limit is performed via two-scale asymptotic expansions on the system of equations thus obtained.

Keywords
homogenization, asymptotic expansions, concentration, elliptic partial differential equations
Mathematical Subject Classification
Primary: 35B27, 35C20, 35J47
Milestones
Received: 12 April 2023
Revised: 14 September 2023
Accepted: 3 October 2023
Published: 20 December 2023

Communicated by Emilio Barchiesi
Authors
Micol Amar
Dipartimento di Scienze di Base e Applicate per l’Ingegneria
University of Rome La Sapienza
Rome
Italy
Afsheen Ayub
Government Degree College for Women, Ayub Research
Faisalabad
Pakistan
Roberto Gianni
Dipartimento di Matematica e Informatica
University of Florence
Firenze
Italy