A HYBRID PARABOLIC AND HYPERBOLIC EQUATION MODEL FOR A POPULATION WITH SEPARATE DISPERSAL AND STATIONARY STAGES: WELL-POSEDNESS AND POPULATION PERSISTENCE

In this paper, we develop a hybrid parabolic and hyperbolic equation model, in which a reaction-diffusion equation governs the random movement and settlement of dispersal individuals, while a first-order hyperbolic equation describes the growth of stationary individuals with age structure. We prove...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 2019-01, Vol.79 (6), p.2265-2287
Main Authors: DENG, KENG, HUANG, QIHUA
Format: Article
Language:English
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Summary:In this paper, we develop a hybrid parabolic and hyperbolic equation model, in which a reaction-diffusion equation governs the random movement and settlement of dispersal individuals, while a first-order hyperbolic equation describes the growth of stationary individuals with age structure. We prove the existence and uniqueness of the solution of the model using the monotone method based on a comparison principle. We study the population persistence criteria in terms of four related measures. We numerically investigate how the interplay between population dispersal, reproduction, settlement, and habitat boundary affects the population persistence.
ISSN:0036-1399
1095-712X
DOI:10.1137/19M124469X