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arXiv · 1801.07095

Mass transport in Fokker-Planck equations with tilted periodic potential

Michael Herrmann·Barbara Niethammer
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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.

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Michael Herrmann, Barbara Niethammer. 2018-01-22. Mass transport in Fokker-Planck equations with tilted periodic potential. https://doi.org/10.1017/s0956792519000251

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