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On interacting populations that disperse to avoid crowding: preservation of segregation. (English) Zbl 0596.35074

Two interacting biological populations which disperse to avoid crowding are considered. The mathematical formulation yields a coupled system of degenerate parabolic equations. Under the assumptions that (i) the populations are sufficiently dense so that continuum theory applies, (ii) the species are undergoing dispersal on a time scale sufficiently small that births and deaths are negligible, the authors prove the existence of solutions, with the initial data related to the situations in which the two populations are segregated for all time. It is also taken that dispersal is a response to population pressure. Under conditional assumptions the asymptotic behaviour of the solutions is studied.
Reviewer: V.Sree Hari Rao

MSC:

35K65 Degenerate parabolic equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
92D25 Population dynamics (general)
35B40 Asymptotic behavior of solutions to PDEs
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