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Asymptotic behavior of reaction–advection–diffusion population models with Allee effect
Author(s) -
Jerez Silvia,
Verdugo Jonathan
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6524
Subject(s) - allee effect , mathematics , uniqueness , advection , monotone polygon , reaction–diffusion system , population , statistical physics , mathematical analysis , physics , demography , sociology , thermodynamics , geometry
In this work, a qualitative analysis is carried out for reaction–advection–diffusion (RAD) systems modeling the interactions between two species with Allee effect. In particular, we study different scenarios: mutualism, competition, and a predator–prey relationship in order to investigate the survival or extinction of both populations. Global existence and uniqueness of positive solutions of the proposed RAD problems are demonstrated. Equilibrium states and asymptotic behavior of solutions are obtained using the monotone method and the upper and lower solutions technique. Numerical simulations by a Crank–Nicolson monotone iterative method of the different asymptotic solution dynamics are shown to illustrate our theoretical results.