Global Dynamics and Patterns of a Gray-Scott Model with Local-Nonlocal Diffusion

Abstract

This paper studies the global existence of component-wise nonnegative solutions of the Gray-Scott model in $\hat{I}\text{c◯}\subset {\mathbb{R}}^n$, $n\ge 1$, 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. We also present the patterns of both local and mixed Gray-Scott models.