Discrete double-porosity models

TL;DR

This paper investigates the homogenization of high-contrast double porosity functionals on a lattice, deriving the limit functional and analyzing the convergence of associated gradient flows.

Contribution

It provides a Gamma-limit characterization for discrete double porosity models and explores the convergence of their gradient flows under periodicity and p-growth conditions.

Findings

Homogenization result for high-contrast double porosity functionals

Explicit description of the limit functional structure

Convergence analysis of the associated gradient flows

Abstract

We study a discrete-to-continuous Gamma-limit of a family of high-contrast double porosity type functionals defined on a scaled integer lattice. Under periodicity and p-growth conditions we prove the homogenization result and describe the structure of the limit functional. Also, we study the convergence of the corresponding gradient flow.