J. Carrillo, M.P. Gualdani, A. Jüngel:

"Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equation in R";^{d}

in: "ASC Report 14/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

A nonlinear degenerate Fokker-Planck equation in the whole space

is analyzed. The existence of solutions to the corresponding implicit

Euler scheme is proved, and it is shown that the semi-discrete solution

converges to a solution of the continuous problem. Furthermore, the

discrete entropy decays monotonically in time. The nonlinearity is

assumed to be of porous-medium type. For the (given) potential,

either a less than quadratic growth condition at infinity is supposed

or the initial datum is assumed to be compactly supported. The proof

is based on regularization and maximum principle arguments. Upper

bounds for the tail behavior in space at infinity are also derived in the

at-most-quadratic growth case.

Fokker-Planck equation, drift-diffusion equation, degenerate

http://www.asc.tuwien.ac.at/preprint/2007/asc14x2007.pdf

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