Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 77, pp. 1-13.

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

Authors: Jesus Ildefonso Diaz (Univ. Complutense de Madrid, Spain)
         David Gomez-Castro   (Univ. Complutense de Madrid, Spain)
         Tatiana A. Shaposhnikova (Moscow State Univ., Moscow, Russia)
         Maria  N. Zubova (Moscow State Univ., Moscow, Russia)

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.

Submitted March 10, 2019. Published June 04, 2019.
Math Subject Classifications: 35B27, 35K57.
Key Words: Critically scaled homogenization; perforated media; 
           dynamical boundary conditions; strange term; nonlocal memory reaction.