Article Contents
Article Contents

# On sufficient conditions for a linearly determinate spreading speed

• 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.

 Citation:

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