A Liouville-type result for some non-cooperative Fisher--KPP systems and nonlocal equations on cylinders
Résumé
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 long-time behavior 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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