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A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions

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Díaz Díaz, Jesús Ildefonso and Gómez Castro, David and Shaposhnikova, Tatiana A. and Zubova, Maria N. (2019) A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions. Electronic Journal of Differential Equations, 2019 (77). 1 - 13. ISSN 1072-6691

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Official URL: https://ejde.math.txstate.edu/Volumes/2019/77/diaz.pdf




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.


Item Type:Article
Uncontrolled Keywords:Critically scaled homogenization; Perforated media; Dynamical boundary conditions; Strange term; Nonlocal memory reaction.
Subjects:Sciences > Physics > Mathematical physics
Sciences > Mathematics > Mathematical analysis
ID Code:63638
Deposited On:18 Jan 2021 17:11
Last Modified:19 Jan 2021 07:55

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