A Liouville-type result for non-cooperative Fisher--KPP systems and nonlocal equations in cylinders - Archive ouverte HAL Access content directly
Journal Articles Acta Applicandae Mathematicae Year : 2020

A Liouville-type result for non-cooperative Fisher--KPP systems and nonlocal equations in cylinders

Abstract

We address the uniqueness of the nonzero stationary state for a reaction-diffusion system of Fisher-KPP type that does not satisfy the comparison principle. Although the uniqueness is false in general, it turns out to be true under biologically natural assumptions on the parameters. This Liouville-type result is then used to characterize the wake of traveling waves. All results are extended to an analogous nonlocal reaction-diffusion equation that contains as a particular case the cane toads equation with bounded traits.
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Dates and versions

hal-02406343 , version 1 (12-12-2019)
hal-02406343 , version 2 (10-01-2020)
hal-02406343 , version 3 (11-03-2020)

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Léo Girardin, Quentin Griette. A Liouville-type result for non-cooperative Fisher--KPP systems and nonlocal equations in cylinders. Acta Applicandae Mathematicae, 2020, 170, pp.123-139. ⟨hal-02406343v3⟩
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