Homogenization of parabolic problems for non-local convolution type operators under non-diffusive scaling of coefficients

2025/06/01 by Piatnitski, Andrey, Zhizhina, Elena
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2506.00872

Abstract

We study homogenization problem for non-autonomous parabolic equations of the form ∂_t u=L(t)u with an integral convolution type operator L(t) that has a non-symmetric jump kernel which is periodic in spatial variables and in time. It is assumed that the space-time scaling of the environment is not diffusive. We show that asymptotically the spatial and temporal evolutions of the solutions are getting decoupled, and the homogenization result holds in a moving frame.

Citations

• Homogenization of non-autonomous operators of convolution type in periodic media
• Homogenization of biased convolution type operators
• Periodic homogenization of non-local operators with a convolution type\n kernel

Related

• Homogenization of non-autonomous evolution problems for convolution type operators in random media
• Homogenization of non-autonomous operators of convolution type in periodic media
• Homogenization of biased convolution type operators
• Periodic homogenization of non-local operators with a convolution type\n kernel
• Stochastic homogenization of nonlinear evolution equations with space-time nonlocality