ON FOKKER-PLANCK EQUATIONS WITH IN- AND OUTFLOW OF MASS

Burger M, Humpert I, Pietschmann JF (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Kinetic and Related Models American Institute of Mathematical Sciences (AIMS)

Book Volume: 13

Pages Range: 249-277

Journal Issue: 2

DOI: 10.3934/krm.2020009

Abstract

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.

Authors with CRIS profile

Martin Burger Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE) Technische Universität Chemnitz DE Germany (DE)

How to cite

APA:

Burger, M., Humpert, I., & Pietschmann, J.-F. (2020). ON FOKKER-PLANCK EQUATIONS WITH IN- AND OUTFLOW OF MASS. Kinetic and Related Models, 13(2), 249-277. https://doi.org/10.3934/krm.2020009

MLA:

Burger, Martin, Ina Humpert, and Jan-Frederik Pietschmann. "ON FOKKER-PLANCK EQUATIONS WITH IN- AND OUTFLOW OF MASS." Kinetic and Related Models 13.2 (2020): 249-277.

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