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Our main interest in this paper is the study of homogenised limit of aparabolic equation with a nonlinear dynamic boundary condition of themicro-scale model set on a domain with periodically place particles. We focuson the case of particles (or holes) of critical diameter with respect to theperiod of the structure. Our main result proves the weak convergence of thesequence of solutions of the original problem to the solution of areaction-diffusion parabolic problem containing a `strange term'. The noveltyof our result is that this term is a nonlocal memory solving an ODE. We provethat the resulting system satisfies a comparison principle.

A nonlocal memory strange term arising in the critical scale homogenisation of a diffusion equation with a dynamic boundary condition