Homogenization of Non-Autonomous Operators of Convolution Type in Periodic Media

A. Piatnitski, E. Zhizhina

2023, v.29, Issue 2, 173-188


The paper deals with periodic homogenization problem for a para\-bo\-lic equation whose elliptic part is a convolution type
operator with rapidly oscillating coefficients. It is assumed that the coefficients are rapidly oscillating periodic functions both
in spatial and temporal variables and that the scaling is diffusive, that is, the scaling factor of the temporal variable
is equal to the square of the scaling factor of the spatial variable.
Under the assumption that the convolution kernel has a finite second moment and that the operator is symmetric in spatial
variables we show that the equation under study admits homogenization, and we prove that the limit operator is a second order
differential parabolic operator with constant coefficients.


Keywords: convolution type operators, periodic homogenization, homogenization of non-autonomous equations


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