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Corrector results for space-time homogenization of nonlinear diffusion

Tomoyuki Oka

Vol. 10 (2022), No. 2, 171–190
DOI: 10.2140/memocs.2022.10.171
Abstract

The present paper concerns a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. The main results consist of corrector results (i.e., strong convergence with corrector terms) for gradients, diffusion fluxes and time-derivatives of solutions without assumptions for smoothness of coefficients. Proofs of the main results are based on the space-time version of the unfolding method, which is deeply concerned with the strong two-scale convergence theory.

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Keywords
space-time homogenization, corrector result, two-scale convergence, unfolding method, fast diffusion equation, porous medium equation, nonlinear diffusion equation
Mathematical Subject Classification
Primary: 35B27
Secondary: 80M40, 47J35
Milestones
Received: 20 January 2022
Revised: 10 July 2022
Accepted: 6 September 2022
Published: 25 October 2022

Communicated by Micol Amar
Authors
Tomoyuki Oka
Graduate School of Science
Tohoku University
Sendai
Japan