A nonlocal Gray-Scott model: well-posedness and diffusive limit

TL;DR

This paper investigates the well-posedness and stability of a nonlocal Gray-Scott model with integrable kernels and demonstrates that solutions converge to the classical model in the diffusive limit.

Contribution

It establishes well-posedness and stability results for the nonlocal Gray-Scott model and shows convergence to the classical system in the diffusive limit.

Findings

Well-posedness in $L_ extinfty$ for the nonlocal model

Stability of the spatially homogeneous steady state

Convergence of solutions to the classical Gray-Scott system in the diffusive limit

Abstract

Well-posedness in $L_\infty$ of the nonlocal Gray-Scott model is studied for integrable kernels, along with the stability of the semi-trivial spatially homogeneous steady state. In addition, it is shown that the solutions to the nonlocal Gray-Scott system converge to those to the classical Gray-Scott system in the diffusive limit.