On the modelling of spatially heterogeneous nonlocal diffusion: deciding factors and preferential position of individuals
We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the link between the two groups of diffusion equations which include both spatial heterogeneity and anisotropy. In particula...
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Veröffentlicht in: | Journal of mathematical biology 2022-04, Vol.84 (5), p.38-38, Article 38 |
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Hauptverfasser: | , , , , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the link between the two groups of diffusion equations which include both spatial heterogeneity and anisotropy. In particular, we introduce the notion of deciding factors which single out a nonlocal diffusion model and typically consist of the
total jump rate
and the
average jump length
. In this framework, we also discuss the dependence of the profile of the steady state solutions on these deciding factors, thus shedding light on the preferential position of individuals. |
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ISSN: | 0303-6812 1432-1416 |
DOI: | 10.1007/s00285-022-01738-y |