Dynamics of non-local lattice systems in ℓ1

Abstract

In this paper, the well-posedness and asymptotic behavior of a non-local lattice system are analyzed in the space ${\ell }^1$. In fact, the analysis is carried out in the subspace ${\ell }_{+}^1$ formed by the nonnegative elements, remaining open the case of the whole space. The same problem has been analyzed recently in the space ${\ell }^2$ (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.