Mathematics > Analysis of PDEs
arXiv:2509.24019 (math)
[Submitted on 28 Sep 2025 (v1), last revised 16 Jun 2026 (this version, v4)]
Abstract:We analyze the Gray-Scott reaction--diffusion system on $\Omega\subset\mathbb{R}^n$ ($n\ge 1$) with mixed diffusion combining local and nonlocal operators. Using semigroup methods and duality estimates, we prove global existence of component-wise nonnegative solutions and establish uniform-in-time bounds. Numerical simulations illustrate pattern formation and highlight qualitative differences between the purely local and mixed-diffusion models.
Submission history
From: Md Shah Alam [view email]
[v1]
Sun, 28 Sep 2025 18:25:39 UTC (991 KB)
[v2]
Thu, 9 Oct 2025 04:42:09 UTC (991 KB)
[v3]
Mon, 15 Jun 2026 17:28:03 UTC (998 KB)
[v4]
Tue, 16 Jun 2026 07:10:11 UTC (998 KB)
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