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math.AP2025
New cost terms through the homogenization of an optimal control problem under dynamic boundary conditions on the microscopic particles
J. I. Díaz, T. A. Shaposhnikova, A. V. Podolskiy
Given an optimal control problem on a heterogeneous body with a periodical structure of particles depending on a small parameter e, we study the asymptotic behavior, as e converges…
math.AP2019
A nonlocal memory strange term arising in the critical scale homogenisation of a diffusion equation with a dynamic boundary condition
Jesús Ildefonso Díaz, David Gómez-Castro, Tatiana A. Shaposhnikova +1
Our main interest in this paper is the study of homogenised limit of a parabolic equation with a nonlinear dynamic boundary condition of the micro-scale model set on a domain with…
math.AP2018
Homogenization of a net of periodic critically scaled boundary obstacles related to reverse osmosis "nano-composite" membranes
Jesús Ildefonso Díaz, David Gómez-Castro, Alexander V. Podolskiy +1
One of the main goals of this paper is to extend some of the mathematical techniques of some previous papers by the authors showing that some very useful phenomenological propertie…