Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Homogenization of Linear Parabolic Equations with a Certain Resonant Matching Between Rapid Spatial and Temporal Oscillations in Periodically Perforated Domains

Homogenization of Linear Parabolic Equations with a Certain Resonant Matching Between Rapid... In this article, we study homogenization of a parabolic linear problem governed by a coefficient matrix with rapid spatial and temporal oscillations in periodically perforated domains with homogeneous Neumann data on the boundary of the holes. We prove results adapted to the problem for characterization of multiscale limits for gradients and very weak multiscale convergence. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Homogenization of Linear Parabolic Equations with a Certain Resonant Matching Between Rapid Spatial and Temporal Oscillations in Periodically Perforated Domains

Lobkova, Tatiana
Acta Mathematicae Applicatae Sinica , Volume 35 (2) – May 15, 2019
Download PDF
19 pages

Loading next page...
 
/lp/springer-journals/homogenization-of-linear-parabolic-equations-with-a-certain-resonant-EytwJ32xSL
Publisher
Springer Journals
Copyright
Copyright © 2019 by The Editorial Office of AMAS & Springer-Verlag GmbH Germany
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-019-0810-1
Publisher site
See Article on Publisher Site

Abstract

In this article, we study homogenization of a parabolic linear problem governed by a coefficient matrix with rapid spatial and temporal oscillations in periodically perforated domains with homogeneous Neumann data on the boundary of the holes. We prove results adapted to the problem for characterization of multiscale limits for gradients and very weak multiscale convergence.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: May 15, 2019

References

  • An extension theorem from connected sets, and homogenization in general periodic domains
    Acerbi, E; Chiado Piat, V; Dal Maso, G; Percivale, D
  • Homogenization and two-scale convergence
    Allaire, G
  • Multi-scale convergence and reiterated homogenization
    Allaire, G; Briane, M
  • Homogenization of the Neumann problem with nonisolated holes
    Allaire, G; Murat, F
  • Derivation of the double porosity model of single phase flow via homogenization theory
    Arbogast, T; Douglas, J; Hornung, U
  • Asymptotic analysis for periodic structures, studies in mathematics and its applications
    Bensoussan, A; Lions, JL; Papanicolaou, G
  • A general compactness result and its application to the two-scale convergence of almost periodic functions
    Casado-Díaz, J; Gayte, I
  • Homogenization in open sets with holes
    Cioranescu, D; Saint Jean Paulin, J
  • The periodic unfolding method in domains with holes
    Cioranescu, D; Damlamian, A; Donato, G; Griso, G; Zaki, R
  • Sur la convergence de solutions d equations paraboliques [On the convergence of solutions of parabolic equations]
    Colombini, F; Spagnolo, S
  • On the application of the homogenization theory to a class of problems arising in fluid mechanics
    Conca, C
  • Nonhomogeneous Neumann problems in domains with small holes
    Conca, C; Donato, P
  • Homogenization and correctors for the heat equation in perforated domains
    Donato, P; Nabil, A
  • Homogenization of semilinear parabolic equations in perforated domains
    Donato, P; Nabil, A
  • Homogenization of the Poisson equation in a porous medium with double periodicity
    Donato, P; Saint Jean Paulin, J
  • Reiterated homogenization of hyperbolic-parabolic equations in domains with tiny holes
    Douanla, H; Tetsadjio, E
  • Homogenization of reaction-diffusion equations in fractured porous media
    Douanla, H; Woukeng, J L
  • Very weak multiscale convergence
    Flodén, L; Holmbom, A; Olsson, M; Persson, J
  • Homogenization of some parabolic operators with several time scales
    Flodén, L; Olsson, M
  • Applied Functional Analysis
    Griffel, DH
  • Homogenization of parabolic equations: an alternative approach and some corrector-type results
    Holmbom, A
  • On two-scale convergence and related sequential compactness topics
    Holmbom, A; Silfver, J; Svanstedt, N; Wellander, N
  • Two-scale convergence
    Lukassen, D; Nguetseng, G; Wall, P
  • Scale convergence in homogenization
    Mascarenhas, ML; Toader, A-M
  • International Workshop on Multi-Scale Analysis and Homogenization
    Nandakumaran, AK
  • Alternative approaches to the two-scale convergence
    Nechvatal, L
  • general convergence result for a functional related to the theory of homogenization
    Nguetseng, G A
  • Σ-convergence of nonlinear parabolic operators
    Nguetseng, G; Woukeng, JL
  • Σ-convergence
    Nguetseng, G; Svanstedt, N
  • Geometric two-scale convergence on forms and its applications to maxwell’s equations
    Pak, HC
  • On the homogenization of the Poisson equation in partially perforated domain with the arbitrary density of cavities and mixed conditions on their boundary
    Oleinik, OA; Shaposhnikova, TA
  • Homogenization of some selected elliptic and parabolic problems employing suitable generalized modes of two-scale convergence
    Persson, J
  • Selected Topics in Homogenization
    Persson, J
  • Homogenization of monotone parabolic problems with several temporal scales
    Persson, J
  • Homogenization of boundary value problems for monotone operators in perforated domains with rapidly oscillating boundary conditions of fourier type
    Piatnitski, A; Rybalko, V
  • G-convergence and homogenization involving operators compatible with two-scale convergence
    Silfver, J
  • Navier-Stokes Equation
    Temam, R
  • Periodic homogenization of nonlinear non-monotone parabolic operators with three time scales
    Woukeng, JL