A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions
Files
Date
2019-06-04
Authors
Diaz, Jesus Ildefonso
Gomez-Castro, David
Shaposhnikova, Tatiana A.
Zubova, Maria
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
Our main interest in this article is the study of homogenized limit of a parabolic equation with a nonlinear dynamic boundary condition of the micro-scale model set on a domain with periodically place particles. We focus on the case of particles (or holes) of critical diameter with respect to the period of the structure. Our main result proves the weak convergence of the sequence of solutions of the original problem to the solution of a reaction-diffusion parabolic problem containing a "strange term". The novelty of our result is that this term is a nonlocal memory solving an ODE. We prove that the resulting system satisfies a comparison principle.
Description
Keywords
Critically scaled homogenization, Perforated media, Dynamical boundary conditions, Strange term, Nonlocal memory reaction
Citation
Díaz, J. I., Gómez-Castro, D., Shaposhnikova, T. A., & Zubova, M. N. (2019). A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions. <i>Electronic Journal of Differential Equations, 2019</i>(77), pp. 1-13.
Rights
Attribution 4.0 International