On sufficient conditions for a linearly determinate spreading speed

Abstract

It is shown how to construct criteria of the form f(u) 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 (0). Some of these criteria improve the classical condition f(u)(0)u, and permit the presence of sharp Allee effects. Inequalities which guarantee the failure of linear determinacy are also presented.