Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010Spectral problems. Issue dedicated to the memory of M. Birman
|Page(s)||390 - 447|
|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: email@example.com
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
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