A nonlocal Gray-Scott model: well-posedness and 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.