Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A note on interacting populations that disperse to avoid crowding

Authors: Morton E. Gurtin and A. C. Pipkin
Journal: Quart. Appl. Math. 42 (1984), 87-94
MSC: Primary 92A15; Secondary 35Q99
DOI: https://doi.org/10.1090/qam/736508
MathSciNet review: 736508
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Abstract: In this note we derive partial differential equations for populations that disperse to avoid crowding, paying particular attention to situations in which the ease of dispersal is not uniform among individuals. We develop equations for the dispersal of a finite number of interacting biological groups and for a single age-structured group, and we give conditions under which the latter equations reduce to the former. In all cases the equations generalize the classical porous flow equation--a degenerate parabolic equation that exhibits a myriad of interesting effects. For the special case of two groups we deduce a simple solution in which the species remain segregated for all time.

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DOI: https://doi.org/10.1090/qam/736508
Article copyright: © Copyright 1984 American Mathematical Society

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