Abstract:
A multiscale homogenization estimate for a parabolic diffusion equation under minimal regularity conditions is proved. This makes it possible to treat the result as an estimate in the operator norm for the difference of the operator exponentials of the initial and homogenized equations.
Citation:
S. E. Pastukhova, “Approximation of the Exponential of a Diffusion Operator with Multiscale Coefficients”, Funktsional. Anal. i Prilozhen., 48:3 (2014), 34–51; Funct. Anal. Appl., 48:3 (2014), 183–197
\Bibitem{Pas14}
\by S.~E.~Pastukhova
\paper Approximation of the Exponential of a Diffusion Operator with Multiscale Coefficients
\jour Funktsional. Anal. i Prilozhen.
\yr 2014
\vol 48
\issue 3
\pages 34--51
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\jour Funct. Anal. Appl.
\yr 2014
\vol 48
\issue 3
\pages 183--197
\crossref{https://doi.org/10.1007/s10688-014-0060-1}
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Linking options:
https://www.mathnet.ru/eng/faa3155
https://doi.org/10.4213/faa3155
https://www.mathnet.ru/eng/faa/v48/i3/p34
This publication is cited in the following 12 articles:
S. E. Pastukhova, “L2-Estimates of Error in Homogenization of Parabolic Equations with Correctors Taken Into Account”, J Math Sci, 2024
S. E. Pastukhova, “L2-otsenki pogreshnosti usredneniya parabolicheskikh uravnenii s uchetom korrektorov”, SMFN, 69, no. 1, Rossiiskii universitet druzhby narodov, M., 2023, 134–151
T. A. Suslina, “Operator-theoretic approach to the homogenization of Schrödinger-type equations with periodic coefficients”, Russian Math. Surveys, 78:6 (2023), 1023–1154
S. E. Pastukhova, “Homogenization Estimates for Parabolic Equations with Correctors”, J Math Sci, 276:1 (2023), 137
S. E. Pastukhova, “Resolvent Approximations in L2-Norm for Elliptic Operators Acting in a Perforated Space”, J Math Sci, 265:6 (2022), 1008
Pastukhova S.E., “On Resolvent Approximations of Elliptic Differential Operators With Locally Periodic Coefficients”, Lobachevskii J. Math., 41:5, SI (2020), 818–838
Pastukhova S.E., “On Resolvent Approximations of Elliptic Differential Operators With Periodic Coefficients”, Appl. Anal., 2020
S. E. Pastukhova, “Homogenization Estimates for Singularly Perturbed Operators”, J Math Sci, 251:5 (2020), 724
S. E. Pastukhova, “The Neumann problem for elliptic equations with multiscale coefficients: operator estimates for homogenization”, Sb. Math., 207:3 (2016), 418–443
V. V. Zhikov, S. E. Pastukhova, “Operator estimates in homogenization theory”, Russian Math. Surveys, 71:3 (2016), 417–511
Pastukhova S.E., “Estimates in homogenization of higher-order elliptic operators”, Appl. Anal., 95:7, SI (2016), 1449–1466
S. E. Pastukhova, R. N. Tikhomirov, “Error Estimates of Homogenization in the Neumann Boundary Problem for an Elliptic Equation with Multiscale Coefficients”, J Math Sci, 216:2 (2016), 325
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