Spreading speeds and monostable waves in a reaction-diffusion model with nonlinear competition

In this paper the wave propagation dynamics of a Lotka-Volterra type of model with cubic competition is studied. The existence of traveling waves and the uniqueness of spreading speeds are established. It is also shown that the spreading speed is equal to the minimal speed for traveling waves. Furthermore, general conditions for the linear or nonlinear selection of the spreading speed are obtained by using the comparison principle and the decay characteristics for traveling waves. By constructing upper solutions, explicit conditions to determine the linear selection of the spreading speed are derived.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Mathematical Physic