Geodesic
$L^2$-estimates of error in homogenization of parabolic equations with correctors taken into account
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 134-151

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We consider second-order parabolic equations with bounded measurable $\varepsilon$-periodic coefficients. To solve the Cauchy problem in the layer $\mathbb{R}^d\times(0,T)$ with the nonhomogeneous equation, we obtain approximations in the norm $\|\cdot\|_{L^2(\mathbb{R}^d\times(0,T))}$ with remainder of order $\varepsilon^2$ as $\varepsilon\to 0.$
Mots-clés : parabolic equations
Keywords: homogenization of solutions, homogenization error, corrector. 
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     author = {S. E. Pastukhova},
     title = {$L^2$-estimates of error in homogenization of parabolic equations with correctors taken into account},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {134--151},
     publisher = {mathdoc},
     volume = {69},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2023_69_1_a8/}
}
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S. E. Pastukhova. $L^2$-estimates of error in homogenization of parabolic equations with correctors taken into account. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 134-151. http://geodesic.mathdoc.fr/item/CMFD_2023_69_1_a8/