Note on quantitative homogenization results for parabolic systems in R-d

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Meshkova , Y 2020 , ' Note on quantitative homogenization results for parabolic systems in R-d ' , Journal of Evolution Equations , vol. 21 , pp. 763–769 . https://doi.org/10.1007/s00028-020-00600-2

Title: Note on quantitative homogenization results for parabolic systems in R-d
Author: Meshkova, Yulia
Contributor: University of Helsinki, Geometric Analysis and Partial Differential Equations
Date: 2020-07-10
Language: eng
Number of pages: 7
Belongs to series: Journal of Evolution Equations
ISSN: 1424-3199
URI: http://hdl.handle.net/10138/329487
Abstract: In L-2(R-d; C-n), we consider a semigroup e(-tA epsilon), t >= 0, generated by a matrix elliptic second- order differential operator A(epsilon) >= 0. Coefficients of A(epsilon) are periodic. depend on X/epsilon, and oscillate rapidly as epsilon -> 0. Approximations for e(-tA epsilon )were obtained by Suslina (Funktsional Analiz i ego Prilozhen 38(4):86-90, 2004) and Suslina (Math Model Nat Phenom 5(4):390-447, 2010) via the spectral method and by Zhikov and Pastukhova (Russ J Math Phys 13(2):224-237, 2006) via the shift method. In the present note, we give another short proof based on the contour integral representation for the semigroup and approximations for the resolvent with two-parametric error estimates obtained by Suslina (2015).
Subject: Homogenization
Convergence rates
Parabolic systems
Trotter-Kato theorem
111 Mathematics
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