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Transition between linear and exponential propagation in Fisher-KPP type reaction-diffusion equations (1111.0408v1)
Published 2 Nov 2011 in math.AP
Abstract: We study the Fisher-KPP equation with a fractional laplacian of order {\alpha} \in (0, 1). We know that the stable state invades the unstable one at constant speed for {\alpha} = 1, and at an exponential in time velocity for {\alpha} \in (0, 1). The transition between these two different speeds is examined in this paper. We prove that during a time of the order - ln(1 - {\alpha}), the propagation is linear and then it is exponential.