期刊
KINETIC AND RELATED MODELS
卷 13, 期 2, 页码 249-277出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/krm.2020009
关键词
Fokker-Planck equations; Entropy methods; Exponential decay; Mass evolution; Logarithmic-Sobolev inequality
资金
- Cells in Motion Cluster of Excellence, Munster - German science foundation DFG [EXC 1003]
- ERC via Grant EU FP7 - ERC Consolidator Grant [615216 LifeInverse]
Motivated by modeling transport processes in the growth of neurons, we present results on (nonlinear) Fokker-Planck equations where the total mass is not conserved. This is either due to in- and outflow boundary conditions or to spatially distributed reaction terms. We are able to prove exponential decay towards equilibrium using entropy methods in several situations. As there is no conservation of mass it is difficult to exploit the gradient flow structure of the differential operator which renders the analysis more challenging. In particular, classical logarithmic Sobolev inequalities are not applicable any more. Our analytic results are illustrated by extensive numerical studies.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据