Analysis and simulation of a nonlocal Gray-Scott model (Q6540268)

This article presents a nonlocal Gray-Scott model posed on a bounded one-dimensional domain with Dirichlet and Neumann boundary conditions. The nonlocal operators are symmetric \(L^1\) convolution kernels that are also positive and spatially extended. The authors prove the existence of weak solutions for small time, and use a finite element method to investigate the effects of (exponential) nonlocal diffusion kernels on the formation of pulse solutions.