Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
|
|
---|---|---|
Page(s) | 390 - 447 | |
DOI | https://doi.org/10.1051/mmnp/20105416 | |
Published online | 12 May 2010 |
Homogenization of a Periodic Parabolic Cauchy Problem in the Sobolev Space H1 (ℝd)
Department of Physics, St. Petersburg State University,
Ul’yanovskaya 3, Petrodvorets,
St. Petersburg, 198504, Russia
* E-mail: suslina@list.ru
In L2(ℝd;
ℂn), we consider a wide class of matrix elliptic second
order differential operators ε
with rapidly oscillating coefficients (depending on x/ε).
For a fixed τ > 0 and small ε > 0, we find
approximation of the operator exponential exp(−
ετ) in the
(L2(ℝd;
ℂn) →
H1(ℝd;
ℂn))-operator norm with an error term of order
ε. In this approximation, the corrector is taken into account. The
results are applied to homogenization of a periodic parabolic Cauchy problem.
Mathematics Subject Classification: 35B27
Key words: periodic differential operators / parabolic Cauchy problem / homogenization / effective operator / corrector
© EDP Sciences, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.