Abstract:We study a class of semilinear reaction-diffusion systems with nonlocal diffusion on a bounded domain $\Omega$ in $\mathbb{R}^n$ with smooth boundary. The initial data is assumed to be component-wise nonnegative and bounded, and the reaction vector field is assumed to be quasi-positive and satisfy a generalized mass control condition. We obtain global existence and uniqueness of component-wise nonnegative solutions, and when the reaction vector field satisfies a linear intermediate sum condition, we establish the uniform boundedness of solutions in $L^p(\Omega)$ for all $2 \le p<\infty$ on bounded time intervals independent of the kernel of the nonlocal diffusion operator. This allows us to generalize a recent diffusive limit result of Laurencot and Walker \cite{laurencot2023nonlocal}. We also analyze a class of $m$-component reaction-diffusion systems in which some of the components diffuse nonlocally and the other components diffuse locally, and establish both global existence and a diffusive limit.
From: Md Shah Alam [view email]
[v1]
Tue, 23 Sep 2025 04:58:06 UTC (1,621 KB)
[v2]
Wed, 8 Oct 2025 15:47:29 UTC (1,621 KB)
[v3]
Mon, 22 Jun 2026 21:59:22 UTC (1,755 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。