T. A. Suslina, “On Homogenization of Periodic Parabolic Systems”, Funktsional. Anal. i Prilozhen., 38:4 (2004), 86–90; Funct. Anal. Appl., 38:4 (2004), 309

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Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 4, Pages 86–90
DOI: https://doi.org/10.4213/faa130 (Mi faa130)

This article is cited in 59 scientific papers (total in 59 papers)

Brief communications

On Homogenization of Periodic Parabolic Systems

T. A. Suslina

St. Petersburg State University, Faculty of Physics

Full-text PDF (191 kB) Citations (59)

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DOI: https://doi.org/10.4213/faa130

Abstract: We study homogenization in the small period limit for a periodic parabolic Cauchy problem in $\mathbb{R}^d$ and prove that the solutions converge in $L_2(\mathbb{R}^d)$ to the solution of the homogenized problem for each $t>0$. For the $L_2(\mathbb{R}^d)$-norm of the difference, we obtain an order-sharp estimate uniform with respect to the $L_2(\mathbb{R}^d)$-norm of the initial value.

Keywords: periodic parabolic system, Cauchy problem, homogenization, effective medium.

Received: 28.08.2004

English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 4, Pages 309–312
DOI: https://doi.org/10.1007/s10688-005-0010-z

Bibliographic databases:

Document Type: Article

UDC: 517.956

Language: Russian

Citation: T. A. Suslina, “On Homogenization of Periodic Parabolic Systems”, Funktsional. Anal. i Prilozhen., 38:4 (2004), 86–90; Funct. Anal. Appl., 38:4 (2004), 309–312

Citation in format AMSBIB

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https://www.mathnet.ru/eng/faa130

https://doi.org/10.4213/faa130

https://www.mathnet.ru/eng/faa/v38/i4/p86

This publication is cited in the following 59 articles:

Jun Geng, Bojing Shi, “Quantitative estimates in almost periodic homogenization of parabolic systems”, Calc. Var., 64:1 (2025)
M. A. Dorodnyi, T. A. Suslina, “Porogovye approksimatsii funktsii ot faktorizovannogo operatornogo semeistva”, Algebra i analiz, 36:1 (2024), 95–161
T. A. Suslina, “Homogenization of elliptic and parabolic equations with periodic coefficients in a bounded domain under the Neumann condition”, Izv. Math., 88:4 (2024), 678–759
S. E. Pastukhova, “L2-Estimates of Error in Homogenization of Parabolic Equations with Correctors Taken Into Account”, J Math Sci, 2024
M. A. Dorodnyi, “High-frequency homogenization of multidimensional hyperbolic equations”, Applicable Analysis, 2024, 1
S. E. Pastukhova, “$L^2$-otsenki pogreshnosti usredneniya parabolicheskikh uravnenii s uchetom korrektorov”, SMFN, 69, no. 1, Rossiiskii universitet druzhby narodov, M., 2023, 134–151
M. A. Dorodnyi, T. A. Suslina, “Homogenization of hyperbolic equations: operator estimates with correctors taken into account”, Funct. Anal. Appl., 57:4 (2023), 364–370
T. A. Suslina, “Operator-theoretic approach to the homogenization of Schrödinger-type equations with periodic coefficients”, Russian Math. Surveys, 78:6 (2023), 1023–1154
A. A. Raev, V. A. Slousch, T. A. Suslina, “Usrednenie odnomernogo periodicheskogo operatora chetvertogo poryadka s singulyarnym potentsialom”, Matematicheskie voprosy teorii rasprostraneniya voln. 53, Zap. nauchn. sem. POMI, 521, POMI, SPb., 2023, 212–239
M. Dorodnyi, “High-Energy Homogenization of a Multidimensional Nonstationary Schrödinger Equation”, Russ. J. Math. Phys., 30:4 (2023), 480
A. A. Miloslova, T. A. Suslina, “Homogenization of the Higher-Order Parabolic Equations with Periodic Coefficients”, J Math Sci, 277:6 (2023), 959
S. E. Pastukhova, “Homogenization Estimates for Parabolic Equations with Correctors”, J Math Sci, 276:1 (2023), 137
V. A. Sloushch, T. A. Suslina, “Operator estimates for homogenization of higher-order elliptic operators with periodic coefficients”, St. Petersburg Math. J., 35:2 (2024), 327–375
T. A. Suslina, “Threshold approximations for the exponential of a factorized operator family with correctors taken into account”, St. Petersburg Math. J., 35:3 (2024), 537–570
Dorodnyi M.A. Suslina T.A., “Homogenization of a Non-Stationary Periodic Maxwell System in the Case of Constant Permeability”, J. Differ. Equ., 307 (2022), 348–388
T. A. Suslina, “Homogenization of the Schrödinger-type equations: operator estimates with correctors”, Funct. Anal. Appl., 56:3 (2022), 229–234
A. A. Mishulovich, “Usrednenie mnogomernykh parabolicheskikh uravnenii s periodicheskimi koeffitsientami na krayu vnutrennei lakuny”, Matematicheskie voprosy teorii rasprostraneniya voln. 52, Zap. nauchn. sem. POMI, 516, POMI, SPb., 2022, 135–175
A. R. Akhmatova, E. S. Aksenova, V. A. Sloushch, T. A. Suslina, “Homogenization of the parabolic equation with periodic coefficients at the edge of a spectral gap”, Complex Variables and Elliptic Equations, 67:3 (2022), 523
A. A. Miloslova, T. A. Suslina, “Usrednenie parabolicheskikh uravnenii vysokogo poryadka s periodicheskimi koeffitsientami”, Differentsialnye uravneniya s chastnymi proizvodnymi, SMFN, 67, no. 1, Rossiiskii universitet druzhby narodov, M., 2021, 130–191
Dorodnyi M.A., “Operator Error Estimates For Homogenization of the Nonstationary Schrodinger-Type Equations: Sharpness of the Results”, Appl. Anal., 2021

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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