Homogenization of biased convolution type operators
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.
The final publication is available at IOS Press through http://dx.doi.org/10.3233/ASY-191533
CitationPiatnitski, A., Zhizhina, E.(2019) Homogenization of biased convolution type operators. Asymptotic Analysis, 115, (3-4), 241-262
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