Contributions to Books:
J. Carrillo, M.P. Gualdani, A. Jüngel:
"Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equation in Rd";
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.
English 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. 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.
Keywords:
Fokker-Planck equation, drift-diffusion equation, degenerate
Electronic version of the publication:
http://www.asc.tuwien.ac.at/preprint/2007/asc14x2007.pdf
Created from the Publication Database of the Vienna University of Technology.