非合作非局部扩散系统的哈纳克型不等式与行波
Harnack-type inequalities and traveling waves for non-cooperative nonlocal diffusion systems
AI总结：
本文针对实数域上弱耦合非局部扩散系统，建立了不依赖耦合矩阵合作性或不可约性的ℓ¹-范数哈纳克型不等式，结合重标度论证等方法，得到了一类带网络结构的非合作非局部扩散系统行波的最小波速存在性及波剖面负无穷处的精确渐近行为。
AI中文摘要：
本文针对实数域上弱耦合非局部扩散系统的正解，建立了全系统的ℓ¹-范数哈纳克型不等式，且不要求耦合矩阵具备合作性或不可约性。作为主要应用，我们将该分析工具与重标度论证相结合，针对一类具有网络结构的非合作非局部扩散系统，建立其行波的最小波速存在性。此外，我们推导了波剖面在负无穷处的精确渐近行为，这一结果通过将哈纳克型不等式与Ikehara定理、Riesz投影相结合，对向量值拉普拉斯变换的奇点展开分析得以实现。
英文摘要：
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.
