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Mass transport in Fokker–Planck equations with tilted periodic potential

Part of: Partial differential equations Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  30 September 2019

MICHAEL HERRMANN Open the ORCID record for MICHAEL HERRMANN [Opens in a new window]  and
BARBARA NIETHAMMER
MICHAEL HERRMANN
Affiliation:
Institute of Computational Mathematics, Technische Universität Braunschweig Universitätsplatz 2, 38106 Braunschweig, Germany email: michael.herrmann@tu-braunschweig.de
BARBARA NIETHAMMER
Affiliation:
Institute of Applied Mathematics, University of Bonn Endenicher Allee 60, 53115 Bonn, Germany email: niethammer@iam.uni-bonn.de
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Abstract

We consider Fokker–Planck equations with tilted periodic potential in the subcritical regime and characterise 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

Fokker–Planck equations with tilted period potentialmodel reduction for multi-scale dynamical systemsasymptotic analysis of singular limits

MSC classification

Primary: 35Q84: Fokker-Planck equations 35B25: Singular perturbations
Secondary: 35B40: Asymptotic behavior of solutions
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 4 , August 2020 , pp. 709 - 736
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Copyright
© Cambridge University Press 2019

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