Parabolic H-convergence and small-amplitude homogenization

Abstract

H-convergence and small-amplitude homogenization is studied for linear parabolic problems with coefficients, which may depend on time. The small-amplitude homogenization consists of taking a sequence of coefficients, whose difference is proportional to a small parameter, and then computing the first correction in the limit. We recall the definition and main results on H-convergence for non-stationary diffusion equation, and prove that the smoothness (with respect to a parameter) is preserved in the process of taking the H-limit, which is essential for our purposes. The explicit expression for the correction is obtained by using a recently introduced parabolic variant of H-mesures.

Keywords:

• H-measures
• parabolic equation
• homogenization

AMS Subject Classifications:

• 35A27
• 35Q40
• 35K05
• 35L45
• 35S05

Acknowledgements

This work is supported in part by the Croatian MZOS through projects 037–0372787–2795 and 037–1193086–3226.