Global Existence and Boundedness of Gray-Scott Model with Local and Nonlocal Diffusion

In this paper, we study the global existence of component-wise nonnegative solutions of the Gray-Scott model in $\Omega \subset \mathbb{R}^n$, $n \ge 1$, with a mixture of both local and nonlocal diffusion operators. We use semigroup theory with duality arguments to establish the global existence and boundedness of solutions of our model.