Abstract and Applied Analysis
Volume 2011 (2011), Article ID 247619, 7 pages
Research Article

New-Type Solutions of the Modified Fischer-Kolmogorov Equation

Department of Mathematics and N.T.I.S., University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic

Received 25 March 2011; Accepted 19 April 2011

Academic Editor: Irena Lasiecka

Copyright © 2011 P. Drábek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove the existence of new-type solutions of the modified Fischer-Kolmogorov equation with slow/fast diffusion and with possibly nonsmooth double-well potential. We show that a certain relation between the rate of the diffusion and the smoothness of the potential may originate new type solutions which do not occur in the classical Fischer-Kolmogorov equation. The main focus of this paper is to show the sensitivity of the mathematical modelling with respect to the chosen form of the diffusion term and the shape of the double-well potential.