Traveling fronts for the generalized Fisher-KPP equation with nonlocal diffusion
Jos\'e Fuentealba, Alexander Quaas
TL;DR
This paper investigates traveling front solutions for a generalized Fisher-KPP equation with nonlocal diffusion, establishing critical speed thresholds, uniqueness, and decay properties of these solutions.
Contribution
It proves the existence of a critical speed for traveling fronts, their uniqueness up to translation, and decay estimates, advancing understanding of nonlocal diffusion models.
Findings
Existence of a critical speed for traveling fronts
Uniqueness of traveling fronts up to translation
Decay estimates for the solutions
Abstract
The aim of this paper is to study the generalized Fisher-KPP equation with nonlocal diffusion. In specific we prove the existence of a critical speed so that traveling front type solutions exist up to this critical speed and non-existence of traveling fronts below this critical value. Moreover, we obtain uniqueness, up to translation, and decay estimates of these traveling fronts.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Nonlinear Differential Equations Analysis · Fractional Differential Equations Solutions