Geodesic
On Homogenization of Periodic Parabolic Systems
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 4, pp. 86-90

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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. 
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     author = {T. A. Suslina},
     title = {On {Homogenization} of {Periodic} {Parabolic} {Systems}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {86--90},
     publisher = {mathdoc},
     volume = {38},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2004_38_4_a9/}
}
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T. A. Suslina. On Homogenization of Periodic Parabolic Systems. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 4, pp. 86-90. http://geodesic.mathdoc.fr/item/FAA_2004_38_4_a9/