Mass transport in Fokker-Planck equations with tilted periodic potential
Analysis of PDEs
2020-03-17 v1
Abstract
We consider Fokker-Planck equations with tilted periodic potential in the subcritical regime and characterize the spatio-temporal dynamics of the partial masses in the limit of vanishing diffusion. Our convergence proof relies on suitably defined substitute masses and bounds the approximation error using the energy-dissipation relation of the underlying Wasserstein gradient structure. In the appendix we also discuss the case of an asymmetric double-well potential and derive the corresponding limit dynamics in an elementary way.
Keywords
Cite
@article{arxiv.1801.07095,
title = {Mass transport in Fokker-Planck equations with tilted periodic potential},
author = {Michael Herrmann and Barbara Niethammer},
journal= {arXiv preprint arXiv:1801.07095},
year = {2020}
}
Comments
23 pages, several figures