Homogenization of a linear parabolic problem with a certain type of matching between the microscopic scales. (Q1627461)

The authors study the periodic homogenization of a linear parabolic problem with space and time (simultaneously) oscillating coefficients, posed in a homogeneous domain with Dirichlet boundary conditions. The main feature of their problem is the choice of the specific scaling in terms of the homogenization parameter \(\epsilon\). The proposed scaling not only links the space and time variables in a peculiar way, but it also allows for the vanishing of the time derivative during the passage to the homogenization limit. The working techniques include the multiscale convergence as well as the very weak multiscale convergence. The paper is written with an exceptional clarity, generously explaining the technical details.