The influence of convection in the existence of wavefronts for biased movements of mixed populations

Abstract

The topic of this talk concerns the existence, uniqueness and regularity properties of wavefronts for degenerate parabolic equations with negative diffusivity, in the framework of a unique treatment. The equations under consideration include the effects of convection; in several cases they extend some known results when convection is missing. For a better understanding, the talk begins with a brief account of results about wavefronts for scalar forward parabolic equations; then, motivations for degenerate forward-backward (forwardbackward- forward) equations are provided. The general results are shown to apply to a recent model proposed for the movement of isolated and grouped organisms in presence of biased convections.