Homogenization of the Cauchy problem for parabolic systems with periodic coefficients
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Yu. M. Meshkova
Translated by: the author - St. Petersburg Math. J. 25 (2014), 981-1019
- DOI: https://doi.org/10.1090/S1061-0022-2014-01326-X
- Published electronically: September 8, 2014
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Abstract:
In $L_2(\mathbb {R}^d;\mathbb {C}^n)$, a class of matrix second order differential operators $\mathcal {B}_\varepsilon$ with rapidly oscillating coefficients (depending on $\mathbf {x}/\varepsilon$) is considered. For a fixed $s>0$ and small $\varepsilon >0$, approximation is found for the operator $\exp (-\mathcal {B}_\varepsilon s)$ in the $(L_2\to L_2)$- and $(L_2\to H^1)$-norm with an error term of order of $\varepsilon$. The results are applied to homogenization of solutions of the parabolic Cauchy problem.References
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Bibliographic Information
- Yu. M. Meshkova
- Affiliation: Department of Physics, St. Petersburg State University, Ul′yanovskaya 3, Petrodvorets, St. Petersburg 198504, Russia
- Email: juliavmeshke@yandex.ru
- Received by editor(s): April 1, 2013
- Published electronically: September 8, 2014
- Additional Notes: Supported by the Ministry of education and science of Russian Federation, project 07.09.2012 no. 8501, 2012-1.5-12-000-1003-016
- © Copyright 2014 American Mathematical Society
- Journal: St. Petersburg Math. J. 25 (2014), 981-1019
- MSC (2010): Primary 35K46
- DOI: https://doi.org/10.1090/S1061-0022-2014-01326-X
- MathSciNet review: 3234842