[KNIHA][B] Nonlinear reaction-diffusion processes for nanocomposites: anomalous improved homogenization

JI Díaz, D Gómez-Castro, TA Shaposhnikova - 2021 - books.google.com
The behavior of materials at the nanoscale is a key aspect of modern nanoscience and
nanotechnology. This book presents rigorous mathematical techniques showing that some …

Operator estimates for homogenization of the Robin Laplacian in a perforated domain

A Khrabustovskyi, M Plum - Journal of Differential Equations, 2022 - Elsevier
Let ε> 0 be a small parameter. We consider the domain Ω ε:= Ω∖ D ε, where Ω is an open
domain in R n, and D ε is a family of small balls of the radius d ε= o (ε) distributed …

Classification of homogenized limits of diffusion problems with spatially dependent reaction over critical-size particles

JI Diaz, D Gomez-Castro, TA Shaposhnikova… - Applicable …, 2019 - Taylor & Francis
The main goal of this paper is to characterize the change of structural behavior (ie the
appearance of the so-called 'strange terms') arising in the homogenization process when …

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

JI Díaz, D Gómez-Castro, TA Shaposhnikova… - arxiv preprint arxiv …, 2019 - arxiv.org
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

JI Díaz, D Gómez-Castro, AV Podolskiy… - Advances in Nonlinear …, 2018 - degruyter.com
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 …

Homogenization of a boundary-value problem in a domain perforated by cavities of arbitrary shape with a general nonlinear boundary condition on their boundaries …

MN Zubova, TA Shaposhnikova - Journal of Mathematical Sciences, 2020 - Springer
A homogenized model is constructed (with rigorous justification) for a boundary-value
problem for the Poisson equation in a periodically perforated domain with a nonlinear Robin …

On the homogenization of an optimal control problem in a domain perforated by holes of critical size and arbitrary shape

JI Díaz, AV Podolskiy, TA Shaposhnikova - Doklady Mathematics, 2022 - Springer
The paper studies the asymptotic behavior of the optimal control for the Poisson type
boundary value problem in a domain perforated by holes of an arbitrary shape with Robin …

Homogenization of boundary value problems in plane domains with frequently alternating type of nonlinear boundary conditions: Critical case

JI Díaz, D Gómez-Castro, AV Podolskiy… - Doklady …, 2018 - Springer
In the present paper we consider a boundary homogenization problem for the Poisson's
equation in a bounded domain and with a part of the boundary conditions of highly …

Appearance of a Nonlocal Monotone Operator in Transmission Conditions when Homogenizing the Poisson Equation in a Domain Perforated Along an (n − 1) …

MN Zubova, TA Shaposhnikova - Journal of Mathematical Sciences, 2021 - Springer
We construct and justify an efficient model arising when homogenizing the Poisson equation
in an ε-periodically perforated domain along an (n− 1)-dimensional manifold by sets of an …

Homogenization Limit for the Diffusion Equation in a Domain Perforated along (n – 1)-Dimensional Manifold with Dynamic Conditions on the Boundary of the …

MN Zubova, TA Shaposhnikova - Doklady Mathematics, 2019 - Springer
The problem of homogenizing the diffusion equation in a domain perforated along an (n–1)-
dimensional manifold with dynamic boundary conditions on the boundary of the perforations …