Homogenization of a Periodic Parabolic Cauchy Problem in the Sobolev Space H1 (ℝd)

T. Suslina¹

¹ Department of Physics, St. Petersburg State University, Ul’yanovskaya 3, Petrodvorets, St. Petersburg, 198504, Russia

Mathematical modelling of natural phenomena, Tome 5 (2010) no. 4, pp. 390-447.

Résumé

In L2(ℝd; ℂn), we consider a wide class of matrix elliptic second order differential operators $\mathcal{A}$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(− $\mathcal{A}$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.

Détail

DOI : 10.1051/mmnp/20105416

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