Homogenization of degenerate parabolic equations with nonlinear Robin reactions in perforated domains
Abstract
We study periodic homogenization of a parabolic equation with linear, degenerate bulk terms in a perforated domain, with a monotone nonlinear Robin reaction of order ε on the pore walls. The storage coefficient may vanish on sets of positive measure, and the diagonal diffusion weights are not bounded below but satisfy an inverse-integrability condition. Under positivity of the mean storage, a quantitative cell-detection estimate yields strong compactness of the states and of the scaled traces. The effective equation has positive storage, a positive-definite diffusion matrix given by a weighted cell problem, and a nonlinear volume reaction obtained by averaging over the pore surface. We also prove a strong weighted-gradient corrector and uniform-in-time convergence of the dissipated and stored energies and of the states in the storage-weighted L2 norm.
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BibTeX
@misc{douanla2026homogenization,
title = {{Homogenization of degenerate parabolic equations with nonlinear Robin reactions in perforated domains}},
author = {Hermann Douanla and Rodrigue Kenne Bogning and Erick Tetsadjio},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37787},
eprint = {2610.37787},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37787},
}
RIS
TY - UNPB
TI - Homogenization of degenerate parabolic equations with nonlinear Robin reactions in perforated domains
AU - Hermann Douanla
AU - Rodrigue Kenne Bogning
AU - Erick Tetsadjio
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37787
UR - https://arxiv.org/abs/2610.37787
AB - We study periodic homogenization of a parabolic equation with linear, degenerate bulk terms in a perforated domain, with a monotone nonlinear Robin reaction of order ε on the pore walls. The storage coefficient may vanish on sets of positive measure, and the diagonal diffusion weights are not bounded below but satisfy an inverse-integrability condition. Under positivity of the mean storage, a quantitative cell-detection estimate yields strong compactness of the states and of the scaled traces. The effective equation has positive storage, a positive-definite diffusion matrix given by a weighted cell problem, and a nonlinear volume reaction obtained by averaging over the pore surface. We also prove a strong weighted-gradient corrector and uniform-in-time convergence of the dissipated and stored energies and of the states in the storage-weighted L^2 norm.
ER -