Abstract
This paper concerns processes described by a nonlinear partial differential equation that is an extension of the Fisher and KPP equations including density-dependent diffusion and nonlinear convection. The set of wave speeds for which the equation admits a wavefront connecting its stable and unstable equilibrium states is characterized. There is a minimal wave speed. For this wave speed there is a unique wavefront which can be found explicitly. It displays a sharp propagation front. For all greater wave speeds there is a unique wavefront which does not possess this property. For such waves, the asymptotic behaviour as the equilibrium states are approached is determined.
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