Details
| Original language | English |
|---|---|
| Pages (from-to) | 3709-3732 |
| Number of pages | 24 |
| Journal | Discrete and Continuous Dynamical Systems - Series S |
| Volume | 16 |
| Issue number | 12 |
| Early online date | Aug 2023 |
| Publication status | Published - Dec 2023 |
Abstract
Well-posedness in L∞ 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.
Keywords
- diffusive limit, Gray-Scott model, nonlocal interaction, stabilization, well-posedness
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Applied Mathematics
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In: Discrete and Continuous Dynamical Systems - Series S, Vol. 16, No. 12, 12.2023, p. 3709-3732.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A Nonlocal Gray-Scott Model
T2 - Well-Posedness and Diffusive Limit
AU - Laurençot, Philippe
AU - Walker, Christoph
N1 - Funding information: Acknowledgments. We thank the referee for useful remarks.
PY - 2023/12
Y1 - 2023/12
N2 - Well-posedness in L∞ 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.
AB - Well-posedness in L∞ 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.
KW - diffusive limit
KW - Gray-Scott model
KW - nonlocal interaction
KW - stabilization
KW - well-posedness
UR - http://www.scopus.com/inward/record.url?scp=85180348111&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2307.10627
DO - 10.48550/arXiv.2307.10627
M3 - Article
AN - SCOPUS:85180348111
VL - 16
SP - 3709
EP - 3732
JO - Discrete and Continuous Dynamical Systems - Series S
JF - Discrete and Continuous Dynamical Systems - Series S
SN - 1937-1632
IS - 12
ER -