Homogenisation of Monotone Parabolic Problems with Several Temporal Scales: The Detailed arXiv e-Print Version

Abstract

In this paper we homogenise monotone parabolic problems with two spatial scales and finitely many temporal scales. Under a certain well-separatedness assumption on the spatial and temporal scales as explained in the paper, we show that there is an H-limit defined by at most four distinct sets of local problems corresponding to slow temporal oscillations, slow resonant spatial and temporal oscillations (the "slow" self-similar case), rapid temporal oscillations, and rapid resonant spatial and temporal oscillations (the "rapid" self-similar case), respectively.