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

Author： Suslina T.  

Publisher： Edp Sciences

E-ISSN： 1760-6101|5|4|390-447

ISSN： 0973-5348

Source： Mathematical Modelling of Natural Phenomena , Vol.5, Iss.4, 2010-05, pp. : 390-447

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Abstract

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.

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