Homogenization of biased convolution type operators
Andrey Lvovich Piatnitski, Е. Г. Жижина, E. Zhizhina · Asymptotic Analysis · 2019
This paper deals with homogenization of parabolic problems for integral convolution type operators with a non-symmetric jump kernel in a periodic elliptic medium. It is shown that the homogenization result holds in moving coordinates. We determine the corresponding effective velocity and prove that the limit operator is a second order parabolic operator with constant coefficients. We also consider the behaviour of the effective velocity in the case of small antisymmetric perturbations of a symmetric kernel, in particular we show that the Einstein relation holds for the studied periodic environment.