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On sufficient conditions for a linearly determinate spreading speed

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  • It is shown how to construct criteria of the form $f(u)\le f'(0)K(u)$ which guarantee that the spreading speed $c^*$ of a reaction-diffusion equation with the reaction term $f(u)$ is linearly determinate in the sense that $c^*=2\sqrt{f'(0)}$. Some of these criteria improve the classical condition $f(u)\le f'(0)u$, and permit the presence of sharp Allee effects. Inequalities which guarantee the failure of linear determinacy are also presented.
    Mathematics Subject Classification: Primary: 35K60, 35B40; Secondary: 92A15.


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    A. N. Kolmogorov, I. G. Petrovski and N. S. Piscounov, Étude de l'équation de la diffusion avec croissance de la quantité de matiére et son application á un probléme biologique, Bull. Univ. d'État á Moscou Ser. Intern., 1 (1937), 1-26.


    M.-H. Wang and M. Kot, Speeds of invasion in a model with strong or weak Allee effects, Mathematical Biosciences, 171 (2001), 83-97.doi: 10.1016/S0025-5564(01)00048-7.

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