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2008 Convergence of an Entropic Semi-discretization for Nonlinear Fokker-Planck Equations in ${\mathbb R}^d$
J. A. Carrillo, M. P. Gualdani, A. Jüngel
Publ. Mat. 52(2): 413-433 (2008).


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.


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J. A. Carrillo. M. P. Gualdani. A. Jüngel. "Convergence of an Entropic Semi-discretization for Nonlinear Fokker-Planck Equations in ${\mathbb R}^d$." Publ. Mat. 52 (2) 413 - 433, 2008.


Published: 2008
First available in Project Euclid: 5 August 2008

zbMATH: 1152.35317
MathSciNet: MR2436732

Primary: 35B40, 35K65

Rights: Copyright © 2008 Universitat Autònoma de Barcelona, Departament de Matemàtiques


Vol.52 • No. 2 • 2008
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