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J. Carrillo, M.P. Gualdani, A. Jüngel:
"Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equations in R^d";
Publicacions Matemàtiques, 52 (2008), S. 413 - 433.

Siehe englischen Abstract.

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 and the solution to the continuous problem is unique. 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 existence 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 parabolic equation