Individual homogenization of nonlinear parabolic operators

Abstract

In this article, we prove an individual homogenization result for a class of almost periodic nonlinear parabolic operators. The spatial and temporal heterogeneities are almost periodic functions in the sense of Besicovitch. The latter allows discontinuities and is suitable for many applications. First, we derive stability and comparison estimates for sequences of G-convergent nonlinear parabolic operators. Furthermore, using these estimates, the individual homogenization result is shown.

Keywords:

• G-convergence
• Non-linear parabolic equations
• Almost periodic functions

Keywords:

• 2000 Mathematics Subject Classifications: 35B27
• 35K55

Acknowledgement

The research of the first author is partially supported by NSF grants DMS-0327713, EIA-0218229 and DOE grant DE-FG02-05ER25669.