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

Philippe Laurençot; Christoph Walker

doi:10.3934/dcdss.2023158

Article Contents

2023, Volume 16, Issue 12: 3709-3732. Doi: 10.3934/dcdss.2023158

This issue Previous Article Degenerate diffusion with Preisach hysteresis Next Article Large time behavior of solutions for a PDE model for compressible elastic curve

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

Philippe Laurençot^1, and
Christoph Walker^2,

1.
Laboratoire de Mathématiques (LAMA) UMR 5127, Université Savoie Mont Blanc, CNRS, F–73000 Chambéry, France
2.
Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, D–30167 Hannover, Germany

Dedicated to Pierluigi Colli on the occasion of his 65th birthday

Received: July 2023

Revised: August 2023

Early access: August 28, 2023

Published online: August 28, 2023

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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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Mathematics Subject Classification: Primary: 35A01, 45J05; Secondary: 35B40, 35K57.

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References

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