Upscaled Equations for the Fokker–Planck Diffusion Through Arrays of Permeable and of Impermeable Inclusions
Year: 2025
Type: article
Abstract: We study the Fokker–Planck diffusion equation with diffusion coefficient depending periodically on the space variable. Inside a periodic array of inclusions the diffusion coefficient is reduced by a factor called the diffusion magnitude. We find the upscaled equations obtained by taking both the degeneration and the homogenization limits in which the diffusion magnitude and the scale of the periodicity tends, respectively, to zero. Different behaviors, classified as pure diffusion, diffusion with mass deposition, and absence of diffusion, are found depending on the order in which the two limits are taken and on the ratio between the size of the inclusions and the scale of the periodicity.
Source: Asymptotic Analysis
Institution: Sapienza University of Rome
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407613496