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

Philippe Laurençot; Christoph Walker

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arXiv · 2307.10627

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

Philippe Laurençot·Christoph Walker

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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.

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Philippe Laurençot, Christoph Walker. 2023-07-20. A nonlocal Gray-Scott model: well-posedness and diffusive limit. https://arxiv.org/abs/2307.10627

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