• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Homogenization of a lubrication problem in oscillating domain by two-scale convergence method
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
August 11, 2026
‘The Peak of Stupidity and ‘The Valley of Despair: HSE Economists Propose an Explanation for the Dunning–Kruger Effect
The Dunning–Kruger effect, which describes a sharp surge in self-confidence among beginners followed by an equally rapid decline as they gain experience, can be explained by the nature of the learning process and the acquisition of new knowledge. This conclusion was reached by Andrey Vorchik of the HSE Faculty of Economic Sciences together with independent researcher Murat Mamyshev. They developed a mathematical model of learning and demonstrated how subjective confidence is formed and changes as knowledge accumulates, as well as how teachers can reduce the ‘valley of despair’ experienced by learners.
July 24, 2026
‘I Like Self-Fulfilling Prophecies
Andrey Vorchik studies happiness, delivers popular science lectures, and believes that science should address social issues as well. In an interview for the Young Scientists of HSE University project, he spoke about how emotions influence decision-making, the Bermuda Triangle formed by the bathroom, refrigerator, and bed, and the ideal formula for education.
July 24, 2026
'Physics Is What the World Is Literally Built On'
Physicist Nina Dzhanayeva, recipient of a Vladimir Potanin Foundation scholarship, focuses her research on nanophotonics. In this interview for the HSE Young Scientists project, she discusses nanowells, scientific intuition, and how physics can help in making frangipane cream puffs.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Homogenization of a lubrication problem in oscillating domain by two-scale convergence method

Buletinul Academiei de Ştiinţe a Republicii Moldova. 2021. No. 1-2. P. 31–68.
Королев А. В., Koroleva Y.

In present paper we do a homogenization with respect to a small parameter of a boundary-value problem describing fluid flow between two moving in space and time rough surfaces. The two-scale convergence method was used to justify the behavior of the flow in the limit.

Language: English
Keywords: homogenization
Similar publications
Культурная глобализация: сценарии гомогенизации и гибридизации
Сехлеян С. А., Социология. Журнал Российской социологической ассоциации 2021 № 5 С. 165–170
CULTURAL GLOBALIZATION: HOMOGENIZATION AND HYBRIDIZATION SCENARIOS The phenomenon of globalization is a process that affects the material and spiritual aspects of life - economics, demography and politics, as well as culture. Based on this, globalization is an object of study not only in social sciences, but also in branches of knowledge - economics, politics, international relations ...
Added: July 16, 2024
Academic excellence through homogenization? Gaining legitimacy from the strategic positioning of top-ranked universities
Pavlyutkin I., Makareva A., , in: The Ambivalence of Power in the Twenty-First Century Economy: Cases from Russia and beyond.: L.: UCL Press, 2022. Ch. 12 P. 237–260.
Added: August 30, 2022
On Friedrichs-type inequalities in domains rarely perforated along the boundary.” Journal of Inequalities and Applications
Koroleva Y., Chechkin G. A., Persson L. -., Journal of Inequalities and Applications 2011 No. 2011 Article 129
This article is devoted to the Friedrichs inequality, where the domain is periodically perforated along the boundary. It is assumed that the functions satisfy homogeneous Neumann boundary conditions on the outer boundary and that they vanish on the perforation. In particular, it is proved that the best constant in the inequality converges to the best ...
Added: October 18, 2021
Limit behaviour of diffusion in high-contrast periodic media and related Markov semigroups
Piatnitski A., Pirogov S. A., Zhizhina E., Applicable Analysis 2019 Vol. 98 No. 1-2 P. 217–231
The goal of the paper is to describe the large time behaviour of a symmetric diffusion in a high-contrast periodic environment and to characterize the limit process under the diffusive scaling. We consider separately the C_0 and L^2 settings. ...
Added: December 5, 2020
“Strange term”in homogenization of attractors of reaction–diffusion equation in perforated domain
Bekmaganbetov K., Chechkin G., Chepyzhov V. V., Chaos, Solitons and Fractals 2020 Vol. 140 P. 110208
We consider reaction–diffusion equation in perforated domain, with rapidly oscillating coefficient in boundary conditions. We do not assume any Lipschitz condition for the nonlinear function in the equa- tion, so, the uniqueness theorem for the corresponding initial boundary value problem may not hold for the considered reaction-diffusion equation. We prove that the trajectory attractors of ...
Added: November 11, 2020
The homogenization of diffusion-convection equations in non-periodic structures
Meirmanov A. M., Galtsev O. V., Turkish Journal of Mathematics 2020 Vol. 44 P. 1054–1064
We consider the homogenization of diffusion-convective problems with given divergence-free velocities in nonperiodic structures defined by sequences of characteristic functions the first sequence . These quence of concentration the second sequence is uniformly bounded in the space of square-summable functions with square-summable derivatives with respect to spatial variables. At the same time, the sequence of ...
Added: October 30, 2020
Об усредненных уравнениях фильтрации в двух областях с общей границей
Мейрманов А. М., Гальцев О. В., Гриценко С. А., Известия РАН. Серия математическая 2019 Т. 83 № 2 С. 142–173
We consider an initial-boundary value problem describing the process of filtration of a weakly viscous fluid in two distinct porous media with common boundary. We prove, at the microscopic level, the existence and uniqueness of a generalized solution of the problem on the joint motion of two incompressible elastic porous (poroelastic) bodies with distinct Lamé constants and ...
Added: October 30, 2020
The Muskat problem and related topics
Meirmanov A. M., Galtsev O. V., Lithuanian Mathematical Journal 2018 Vol. 58 P. 284–308
In the paper, we consider the evolution of the free boundary separating two immiscible viscous fluids with different constant densities in an absolutely rigid solid body and in an elastic skeleton. The motion of the liquids is described by the Stokes equations driven by the input pressure and the force of gravity. For flows in ...
Added: October 30, 2020
Quantized tensor FEM for multiscale problems: diffusion problems in two and three dimensions
Kazeev V., Oseledets I., Rakhuba M. et al., / Series math "arxiv.org". 2020.
Homogenization in terms of multiscale limits transforms a multiscale problem with n+1 asymptotically separated microscales posed on a physical domain D⊂ℝd into a one-scale problem posed on a product domain of dimension (n+1)d by introducing n so-called "fast variables". This procedure allows to convert n+1 scales in d physical dimensions into a single-scale structure in (n+1)d dimensions. We prove here that both the original, physical multiscale problem and the ...
Added: October 20, 2020
Particle Simulation for Predicting Effective Properties of Short Fiber Reinforced Composites
Skoptsov K. A., Sheshenin S., Galatenko V. V. et al., International Journal of Applied Mechanics 2016 Vol. 8 No. 2 P. 1650016-01–1650016-18
We present a method for evaluating elastic properties of a composite material produced by molding a resin filled with short elastic fibers. A flow of the filled resin is simulated numerically using a mesh-free method. After that, assuming that spatial distribution and orientation of fibers are not significantly changed during polymerization, effective elastic moduli of ...
Added: May 22, 2016
Осреднение в задаче о длинных волнах на воде над участком дна с быстрыми осцилляциями
Grushin V. V., Dobrokhotov S. Y., Математические заметки 2014 Т. 95 № 3 С. 359–375
The system of equations of gravity surface waves is considered in the case where the basin's bottom is given by a rapidly oscillating function against a background of slow variations of the bottom. Under the assumption that the lengths of the waves under study are greater than  the characteristic length of the basin bottom's oscillations ...
Added: May 21, 2014
Осреднение и дисперсионные эффекты в задаче о распространении волн, порожденных локализованным источником
Grushin V. V., Dobrokhotov S. Y., Сергеев С. А., Труды Математического института им. В.А. Стеклова РАН 2013 Т. 281 С. 170–187
We construct asymptotic solutions to the wave equation with velocity rapidly oscillating a smoothly varying background and with localized initial perturbations. First, using adiabatic approximation in the operator form, we perform homogenization that leads to a linearized Boussinesq-type equation with smooth coefficients and weak “anomalous” dispersion. Then, asymptotic solutions to this and, as a consequence, ...
Added: October 11, 2013
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit