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

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-07-20 DOI:10.3934/dcdss.2023158

Philippe Laurencçot, Christoph Walker

引用次数: 0

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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非定域Gray-Scott模型:适定性和扩散极限

研究了可积核的非定域Gray-Scott模型在$L_\infty$上的适定性，以及半平凡空间齐次稳态的稳定性。此外，还证明了非局部Gray-Scott系统的解在扩散极限下收敛于经典Gray-Scott系统的解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete and Continuous Dynamical Systems-Series S MATHEMATICS, APPLIED-

CiteScore

3.70

自引率

5.60%

发文量

177

期刊介绍： Series S of Discrete and Continuous Dynamical Systems only publishes theme issues. Each issue is devoted to a specific area of the mathematical, physical and engineering sciences. This area will define a research frontier that is advancing rapidly, often bridging mathematics and sciences. DCDS-S is essential reading for mathematicians, physicists, engineers and other physical scientists. The journal is published bimonthly.