6 papers
Homogenization of Dynamic Signorini-Type Problems on Critically Oscillating Boundaries under Time-Periodic Forcing
J. I. Diaz, A. V. Podolskyi, T. A. Shaposhnikova
We study the homogenization, in the critical scaling regime, of a boundary value problem with a nonlinear dynamic Signorini-type condition posed on a rapidly oscillating portion of…
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…
New unexpected limit operators for homogenizing optimal control parabolic problems with dynamic reaction flow on the boundary of critically scaled particles
Jesus Ildefonso Diaz, Alexander V. Podolskiy, Tatiana A. Shaposhnikova
We pass to the limit in the homogenization of an optimal control problem associated with a parabolic equation with a dynamic boundary condition. New unexpected terms appear due to…
Boundary control and homogenization: optimal climatization through smart double skin boundaries
J. I. Díaz, A. V. Podolskiy, T. A. Shaposhnikova
We consider the homogenization of an optimal control problem in which the control is placed on a part of the boundary and the spatial domain contains a thin layer of "small particl…
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…
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…