On Fokker-Planck equations with in- and outflow of mass
- 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.
| Author: | Martin Burger, Ina Humpert, Jan-Frederik PietschmannORCiDGND |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/102093 |
| ISSN: | 1937-5077OPAC |
| Parent Title (English): | Kinetic & Related Models |
| Publisher: | American Institute of Mathematical Sciences (AIMS) |
| Place of publication: | Springfield, MO |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2020 |
| Release Date: | 2023/02/20 |
| Tag: | Modeling and Simulation; Numerical Analysis |
| Volume: | 13 |
| Issue: | 2 |
| First Page: | 249 |
| Last Page: | 277 |
| DOI: | https://doi.org/10.3934/krm.2020009 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Inverse Probleme |
