M. N. Zubova

Lomonosov Moscow State University

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ТА

Т. А. Шапошникова

Lomonosov Moscow State University

Jesús Ildefonso Díaz Díaz

Universidad Complutense de Madrid

David Gómez‐Castro

Universidad Autónoma de Madrid

M. E. Pérez

Universidad de Cantabria

D. Gómez

Universidad de Cantabria

МЛ

М. Лобо

Science Oxford

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Universidad de Cantabria

Universidad Complutense de Madrid

Instituto de Hortofruticultura Subtropical y Mediterránea "La Mayora"

Universidad Autónoma de Madrid

Science Oxford

Mesoamerican University

Nicolaus Copernicus University

University of Augsburg

Institute of Mathematical Sciences

Real Academia Española

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

DOAJ (DOAJ: Directory of Open Access Journals) (2019)

Jesús Ildefonso Díaz Díaz David Gómez‐Castro Т. А. Шапошникова M. N. Zubova

Homogenization

Dynamic equation

Reaction–diffusion system

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Citations (0)

Homogenization problem for a parabolic variational inequality with constraints on subsets situated on the boundary of the domain

Networks and Heterogeneous Media (2008)

Т. А. Шапошникова M. N. Zubova

This paper is aimed at a homogenization problem for a parabolic variational inequality with unilateral constraints. The constraints on solutions are imposed on disk-shaped subsets belonging to the boundary of the domain and forming a periodic structure, so that one has a problem with rapidly oscillating boundary conditions on a part of the boundary. Under certain conditions on the relation between the period of the structure and the radius of the disks, the homogenized problem is obtained. With the help of special auxiliary functions, the solutions of the original variational inequalities are shown to converge to the solution of the homogenized problem in Sobolev space as the period of the structure tends to zero.

Homogenization

10.3934/nhm.2008.3.675

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Citations (7)

Homogenization of A Boundary-Value Problem in A Domain Perforated by Cavities of Arbitrary Shape with A General Nonlinear Boundary Condition On Their Boundaries: The Case of Critical Values of the Parameters

Journal of Mathematical Sciences (2019)

M. N. Zubova Т. А. Шапошникова

Homogenization

Poisson's equation

Boundary values

10.1007/s10958-019-04616-z

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Citations (7)

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

Doklady Mathematics (2019)

M. N. Zubova Т. А. Шапошникова

Homogenization

Manifold (fluid mechanics)

10.1134/s1064562419030049

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Citations (9)

Averaging of boundary-value problems for the Laplace operator in perforated domains with a nonlinear boundary condition of the third type on the boundary of cavities

Journal of Mathematical Sciences (2013)

M. N. Zubova Т. А. Шапошникова

Operator (biology)

Poisson's equation

10.1007/s10958-013-1253-5

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Citations (5)

Homogenization of variational inequalities for a biharmonic operator with constraints on subsets ε-periodically placed along a manifold of large dimension

Moscow University Mathematics Bulletin (2007)

M. N. Zubova

Biharmonic equation

Homogenization

Operator (biology)

10.3103/s002713220705004x

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Citations (0)

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

arXiv (Cornell University) (2019)

Jesús Ildefonso Díaz Díaz David Gómez‐Castro Т. А. Шапошникова M. N. Zubova

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 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.

Dynamic equation

10.48550/arxiv.1905.11709

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Citations (0)

Homogenization of the variational inequality corresponding to a problem with rapidly varying boundary conditions

Mathematical Notes (2007)

M. N. Zubova Т. А. Шапошникова

Homogenization

10.1134/s0001434607090246

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Citations (6)

Homogenization of variational inequalities for the biharmonic operator with constraints on ɛ-periodically arranged subsets