Asymptotic properties of nonlinear diffusion, nonlinear drift-diffusion, and nonlinear reaction-diffusion equations
Article first published online: 14 JUN 2004
Copyright © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Annalen der Physik
Volume 13, Issue 7-8, pages 461–469, July 2004
How to Cite
Frank, T.D. (2004), Asymptotic properties of nonlinear diffusion, nonlinear drift-diffusion, and nonlinear reaction-diffusion equations. Ann. Phys., 13: 461–469. doi: 10.1002/andp.200410089
- Issue published online: 14 JUN 2004
- Article first published online: 14 JUN 2004
- Manuscript Accepted: 5 APR 2004
- Manuscript Received: 3 MAR 2004
- nonlinear diffusion equations;
- nonlinear reaction-diffusion equations;
- nonlinear Fokker-Planck equations.
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.