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Homogenization of a Periodic Parabolic Cauchy Problem in theSobolev Space H 1(ℝd )

Published online by Cambridge University Press:  12 May 2010

T. Suslina
T. Suslina*
Affiliation:
Department of Physics, St. Petersburg State University, Ul’yanovskaya 3, Petrodvorets, St. Petersburg, 198504, Russia
*
* E-mail: suslina@list.ru
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Abstract

In L 2(ℝd ;ℂn ), we consider a wide class of matrix elliptic secondorder differential operators $\mathcal{A}$ εwith rapidly oscillating coefficients (depending on x/ε).For a fixed τ > 0 and small ε > 0, we findapproximation of the operator exponential exp(− $\mathcal{A}$ ε τ) in the(L 2(ℝd ;ℂn ) →H 1(ℝd ;ℂn ))-operator norm with an error term of orderε. In this approximation, the corrector is taken into account. Theresults are applied to homogenization of a periodic parabolic Cauchy problem.

Keywords

periodic differential operatorsparabolic Cauchy problemhomogenizationeffective operatorcorrector
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 4: Spectral problems. Issue dedicated to the memory of M. Birman , 2010 , pp. 390 - 447
Copyright
© EDP Sciences, 2010

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Footnotes

To the memory of my dear Teacher Mikhail Shlemovich Birman

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