Dispersal towards food: the singular limit of an Allen-Cahn equation

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The effect of dispersal under heterogeneous environment is studied in terms of the singular limit of an Allen-Cahn equation. Since biological organisms often slow down their dispersal if food is abundant, a food metric diffusion is taken to include such a phenomenon. The migration effect of the problem is approximated by a mean curvature flow after taking the singular limit which now includes an advection term produced by the spatial heterogeneity of food distribution. It is shown that the interface moves towards a local maximum of the food distribution. In other words, the dispersal taken in the paper is not a trivialization process anymore, but an aggregation one towards food.
Publisher
SPRINGER HEIDELBERG
Issue Date
2018-02
Language
English
Article Type
Article
Keywords

INHOMOGENEOUS REACTION TERM; REACTION-DIFFUSION EQUATION; MODEL; CHEMOTAXIS; PROPAGATION; INTERFACES; MOTION; SYSTEM

Citation

JOURNAL OF MATHEMATICAL BIOLOGY, v.76, no.3, pp.531 - 565

ISSN
0303-6812
DOI
10.1007/s00285-017-1150-5
URI
http://hdl.handle.net/10203/240139
Appears in Collection
MA-Journal Papers(저널논문)
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