44 citations · 81 across the 22 of their papers we have counts for
3 papers · 1 filter
Homogenization of nonlocal equations in randomly evolving media. Diffusion approximation
Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier
The paper deals with homogenization and higher order approximations of solutions to nonlocal evolution equations of convolution type whose coefficients are periodic in the spatial…
Asymptotic decomposition of solutions to parabolic equations with a random microstructure
Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier
We consider a Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variables and random stationar…
On the fundamental solution of heat and stochastic heat equations
Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier
We consider the generic divergence form second order parabolic equation with coefficients that are regular in the spatial variables and just measurable in time. We show that the sp…