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.

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Author:Martin Burger, Ina Humpert, Jan-Frederik PietschmannORCiDGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/102093
Parent Title (English):Kinetic & Related Models
Publisher:American Institute of Mathematical Sciences (AIMS)
Place of publication:Springfield, MO
Year of first Publication:2020
Release Date:2023/02/20
Tag:Modeling and Simulation; Numerical Analysis
First Page:249
Last Page:277
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Inverse Probleme