Limit behaviour of diffusion in high-contrast periodic media and related Markov semigroups^*

* This paper is dedicated to the memory of Professor Vassily Zhikov. Homogenization and high-contrast media were among his favourite subjects.

ABSTRACT

The goal of the paper is to describe the large time behaviour of a symmetric diffusion in a high-contrast periodic environment and to characterize the limit process under the diffusive scaling. We consider separately the $C_0$ and $L^2$ settings.

KEYWORDS:

• Homogenization
• limit theorem
• high-contrast media
• Markov process

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 60F05
• 60J25
• 60J60
• 35B27

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

* This paper is dedicated to the memory of Professor Vassily Zhikov. Homogenization and high-contrast media were among his favourite subjects.

Additional information

Funding

The research was performed at the Institute for Information Transmission Problems with the financial support of the Russian Science Foundation, project No. 14-50-00150.