Long-time dynamics of the Fisher-KPP equation with nonlocal diffusion and free boundary

Abstract: We consider the Fisher-KPP equation with free boundary and "nonlocal diffusion". We show the problem is well-posed, and its long-time dynamical behavior is governed by a spreading-vanishing dichotomy. Moreover, we completely determine the spreading profile, which may have a finite spreading speed determined by a semi-wave problem, or have infinite spreading speed (accelerated spreading), according to whether a threshold condition on the kernel function is satisfied. Further more, for some typical kernel functions, we obtain sharp estimates of the spreading speed (whether finite or infinite).

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysis

Audience: researchers in the topic

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