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Article type: Research Article
Authors: Piatnitski, A.a; b; * | Zhizhina, E.b
Affiliations: [a] The Arctic University of Norway, Campus Narvik, P.O. Box 385, Narvik 8505, Norway | [b] Institute for Information Transmission Problems of RAS, 19, Bolshoi Karetnyi per. build. 1, 127051 Moscow, Russia. E-mails: [email protected], [email protected]
Correspondence: [*] Corresponding author. E-mail: [email protected].
Abstract: 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.
Keywords: Homogenization in moving coordinates, periodic medium, non-local operator, non-symmetric convolution kernel
DOI: 10.3233/ASY-191533
Journal: Asymptotic Analysis, vol. 115, no. 3-4, pp. 241-262, 2019
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