ON SUFFICIENT CONDITIONS FOR A LINEARLY DETERMINATE SPREADING SPEED

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 root f'(0). Some of these criteria improve the classical condition f (u) <= f'(0)u, and permit the presence of sharp Allee effects. Inequalities which guarantee the failure of linear determinacy are also presented.