Journal
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
Volume 31, Issue 4, Pages 709-736Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0956792519000251
Keywords
Fokker-Planck equations with tilted period potential; model reduction for multi-scale dynamical systems; asymptotic analysis of singular limits
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Funding
- Deutsche Forschungsgemeinschaft within the Collaborative Research Center 1060 'The Mathematics of Emergent Effects'
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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.
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