Global analysis of the Gray–Scott model with fractional–classical diffusion

We analyze the Gray–Scott reaction–diffusion system on Ω⊂Rn (n≥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 bounds. Numerical simulations illustrate pattern formation and highlight qualitative differences between the purely local and mixed-diffusion models.