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arXiv · 2608.11107

Harnack-type inequalities and traveling waves for non-cooperative nonlocal diffusion systems

Bo-Sheng Chen·Chang-Hong Wu
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Abstract

In this paper, we establish a system-wide $\ell^1$-norm Harnack-type inequality for positive solutions of weakly coupled nonlocal diffusion systems on $\mathbb{R}$, without assuming cooperativity or irreducibility of the coupling matrices. As a primary application, we integrate this analytical tool with a rescaling argument to establish the existence of the minimal wave speed for traveling waves for a class of non-cooperative nonlocal diffusion systems with network structures. Furthermore, we derive the precise asymptotic behavior of wave profiles at negative infinity. This is achieved by combining Harnack-type inequalities and Ikehara's theorem with Riesz projections to analyze singularities of vector-valued Laplace transforms.

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Bo-Sheng Chen, Chang-Hong Wu. 2026-08-11. Harnack-type inequalities and traveling waves for non-cooperative nonlocal diffusion systems. https://arxiv.org/abs/2608.11107

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