Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 502, Issue 1, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2021.125232
Keywords
Population dynamics; Predator-prey systems; Parabolic-hyperbolic equations; Nonlocal conservation laws; Nonlocal boundary value problem
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Funding
- Region Bourgogne FrancheComte [OPE-2017-0067]
- Research Project of National Relevance Multiscale Innovative Materials and Structures - Italian Ministry of Education, University and Research (MIUR Prin 2017) [2017J4EAYB]
- Italian Ministry of Education, University and Research under the Programme Department of Excellence [CUPD94I18000260001]
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This study demonstrates the existence and stability of entropy solutions for a predator-prey system, which includes a hyperbolic equation for predators and a parabolic-hyperbolic equation for preys. Existence of solutions is established using the vanishing viscosity method, and stability is proven through a doubling of variables type argument.
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.
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