New-type solutions of the modified Fischer-Kolmogorov equation. (English) Zbl 1221.35043

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.


35B25 Singular perturbations in context of PDEs
35K58 Semilinear parabolic equations
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