An hyperbolic-parabolic predator-prey model involving a vole population structured in age

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:502

Article

Coclite, G. M.¹  Donadello, C.²  Nguyen, T. N. T.² 

[1] Polytech Univ, Dept Mech Math & Management, Via E Orabona 4, I-70125 Bari, Italy

[2] Univ Bourgogne Franche Comte, CNRS UMR6623, Lab Math, 16 Route Gray, F-25030 Besancon, France

关键词: Population dynamics;    Predator-prey systems;    Parabolic-hyperbolic equations;    Nonlocal conservation laws;    Nonlocal boundary value problem;   

DOI  :  10.1016/j.jmaa.2021.125232

来源: Elsevier

【 摘 要 】

We prove existence and stability of entropy solutions for a predator-prey system consisting of an hyperbolic equation for predators and a parabolic-hyperbolic equation for preys. The preys' equation, which represents the evolution of a population of voles as in [2], depends on time, t, age, a, and on a 2-dimensional space variable x, and it is supplemented by a nonlocal boundary condition at a = 0. The drift term in the predators' equation depends nonlocally on the density of preys and the two equations are also coupled via classical source terms of Lotka-Volterra type, as in [4]. We establish existence of solutions by applying the vanishing viscosity method, and we prove stability by a doubling of variables type argument. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free