In this paper, the well-posedness and asymptotic behavior of a non-local lattice system are analyzed in the space ℓ1. In fact, the analysis is carried out in the subspace ℓ+1 formed by the nonnegative elements, remaining open the case of the whole space. The same problem has been analyzed recently in the space ℓ2 (see Y. Li et al., Communications on Pure and Applied Analysis, 23 (2024), 935-960). However, the latter does not allow us to consider non-local terms which are natural in the modeling of reaction–diffusion problems introduced by M. Chipot in the wide literature published on this problem. With the current analysis, it is possible to investigate these interesting situations.

中文翻译：

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[公式省略] 中非局部晶格系统的动力学


在本文中，分析了非局部晶格系统在空间 l1 中的适定性和渐近行为。事实上，分析是在非负元素形成的子空间 l+1 中进行的，在整个空间的情况下保持开放。最近在空间 l2 中分析了同样的问题（参见 Y. Li 等人，纯粹和应用分析通讯，23 （2024），935-960）。然而，后者不允许我们考虑非局部术语，这些术语在 M. Chipot 在关于这个问题的广泛文献中引入的反应-扩散问题建模中是很自然的。通过当前的分析，可以调查这些有趣的情况。