On sufficient conditions for a linearly determinate spreading speed

Hans Weinberger

doi:10.3934/dcdsb.2012.17.2267

Article Contents

2012, Volume 17, Issue 6: 2267-2280. Doi: 10.3934/dcdsb.2012.17.2267

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On sufficient conditions for a linearly determinate spreading speed

Hans Weinberger^1,

1.
School of Mathematics, University of Minnesota, 206 Church Street, Minneapolis, MN 55455

Received: May 31, 2011

Revised: November 30, 2011

Published: August 2012

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Abstract

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.

Keywords:

Reaction-diffusion systems,
spreading speed.

Mathematics Subject Classification: Primary: 35K60, 35B40; Secondary: 92A15.

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References

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