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Transition Fronts in Inhomogeneous Fisher-KPP Reaction-Diffusion Equations (1103.3094v1)
Published 16 Mar 2011 in math.AP
Abstract: We use a new method in the study of Fisher-KPP reaction-diffusion equations to prove existence of transition fronts for inhomogeneous KPP-type non-linearities in one spatial dimension. We also obtain new estimates on entire solutions of some KPP reaction-diffusion equations in several spatial dimensions. Our method is based on the construction of sub- and super-solutions to the non-linear PDE from solutions of its linearization at zero.