Geodesic
Approximations of the operator exponential in a~periodic diffusion problem with drift
Sbornik. Mathematics, Tome 204 (2013) no. 2, pp. 280-306

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A Cauchy problem for a parabolic diffusion equation with 1-periodic coefficients containing first order terms is studied. For the corresponding semigroup we construct approximations in the $L^2$-operator norm on sections $t=\mathrm{const}$ of order $O(t^{-m/2})$ as $t\to\infty$ for $ m=1$ or $m=2$. The spectral method based on the Bloch representation of an operator with periodic coefficients is used. Bibliography: 25 titles.
Keywords: diffusion with drift, operator exponential, homogenization, spectral method, Bloch decomposition of functions. 
@article{SM_2013_204_2_a6,
     author = {S. E. Pastukhova},
     title = {Approximations of the operator exponential in a~periodic diffusion problem with drift},
     journal = {Sbornik. Mathematics},
     pages = {280--306},
     publisher = {mathdoc},
     volume = {204},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_2_a6/}
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S. E. Pastukhova. Approximations of the operator exponential in a~periodic diffusion problem with drift. Sbornik. Mathematics, Tome 204 (2013) no. 2, pp. 280-306. http://geodesic.mathdoc.fr/item/SM_2013_204_2_a6/