Convergence to travelling waves in the Fisher-Kolmogorov equation with a non-Lipschitzian reaction term


  • Pavel Drabek Department of Mathematics and NTIS, University of West Bohemia, Pilsen


We consider the semilinear Fisher-Kolmogorov-Petrovski-Piscounov equation for the advance of an advantageous gene in biology.В  In contrast with previous works on this topic, we relax the differentiability hypothesis on f to being only Holder-continuous and one-sided' Lipschitz-continuous.В  In particular, our hypotheses allow for В  singular derivatives.В  This type of a reaction functionВ  f has been studied extensively in biological models of various kinds of logistic growth by A. Tsoularis and J. Wallace.
The fact that reaction functionВ  is not smooth allows for the introduction of travelling waves with a new profile. We study existence and uniqueness of this new profile, as well as a long-time asymptotic behavior of the solutions of the Cauchy problem to a travelling wave. Presented results are based on joint research with P. Takac.






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