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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Figure 3.
Evolution over Time of the Particle Concentration: The time evolution of
Figure 4.
Relative Entropy: The relative entropy (15) for the one dimensional version of (3) for the initial particle concentration
Figure 7.
Evolution over Time of the Particle Concentration: Solution of (26) in comparison to the calculated stationary solution
Figure 9.
Evolution over Time of the Particle Concentration:
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