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Mass transport in Fokker–Planck equations with tilted periodic potential
European Journal of Applied Mathematics ( IF 1.9 ) Pub Date : 2019-10-01 , DOI: 10.1017/s0956792519000251
MICHAEL HERRMANN , BARBARA NIETHAMMER

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.

中文翻译:

具有倾斜周期势的 Fokker-Planck 方程中的质量传输

我们考虑在亚临界状态下具有倾斜周期势的 Fokker-Planck 方程,并在消失扩散的极限下表征部分质量的时空动力学。我们的收敛证明依赖于适当定义的替代质量,并使用底层 Wasserstein 梯度结构的能量耗散关系限制近似误差。在附录中,我们还讨论了不对称双阱势的情况,并以基本的方式推导出了相应的极限动力学。
更新日期:2019-10-01
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