Drábek, P. New-type solutions of the modified Fischer-Kolmogorov equation. (English) Zbl 1221.35043 Abstr. Appl. Anal. 2011, Article ID 247619, 7 p. (2011). Summary: 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. MSC: 35B25 Singular perturbations in context of PDEs 35K58 Semilinear parabolic equations Keywords:slow diffusion; fast diffusion; nonsmooth double-well potential PDF BibTeX XML Cite \textit{P. Drábek}, Abstr. Appl. Anal. 2011, Article ID 247619, 7 p. (2011; Zbl 1221.35043) Full Text: DOI OpenURL References: [1] L. A. Peletier and W. C. Troy, Spatial Patterns, Higher Order Models in Physics and Mechanics, Progress in Nonlinear Differential Equations and Their Applications Vol. 45, Birkhäuser, Boston, Mass, USA, 2001. · Zbl 1076.34515 [2] Z. X. Chen and B. Y. Guo, “Analytic solutions of the Nagumo equation,” IMA Journal of Applied Mathematics, vol. 48, no. 2, pp. 107-115, 1992. · Zbl 0774.35085 [3] E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, NY, USA, 1955. · Zbl 0064.33002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.