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Asymptotic properties of nonlinear diffusion, nonlinear drift‐diffusion, and nonlinear reaction‐diffusion equations
Author(s) -
Frank T.D.
Publication year - 2004
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200410089
Subject(s) - anomalous diffusion , statistical physics , nonlinear system , cascade , diffusion , stochastic process , gaussian , physics , lévy flight , turbulence , probability density function , probability and statistics , mathematics , statistics , computer science , mechanics , quantum mechanics , random walk , knowledge management , chemistry , innovation diffusion , chromatography
We review a Fokker‐Planck approach to nonlinear evolution equations such as nonlinear diffusion equations and nonlinear drift‐diffusion equations and extend this approach to nonlinear reaction‐diffusion equations. Using this Fokker‐Planck approach along with appropriately defined entropy and free energy measures, we show that transient solutions converge to stationary ones in the long time limit. Implications for bifurcation theory are also addressed.