6533b859fe1ef96bd12b82ef
RESEARCH PRODUCT
AN HYPERBOLIC-PARABOLIC PREDATOR-PREY MODEL INVOLVING A VOLE POPULATION STRUCTURED IN AGE
Giuseppe Maria CocliteT.n.t. NguyenC. Donadellosubject
Population dynamicsPopulationType (model theory)Space (mathematics)01 natural sciencesStability (probability)Predator-prey systemsNonlinear Sciences::Adaptation and Self-Organizing SystemsApplied mathematicsQuantitative Biology::Populations and Evolution[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicseducationEntropy (arrow of time)Variable (mathematics)Mathematicseducation.field_of_studyApplied Mathematics010102 general mathematicsNonlocal boundary value problemNonlocal conservation lawsParabolic-hyperbolic equationsTerm (time)010101 applied mathematicsPopulation dynamics Predator-prey systems Parabolic-hyperbolic equations Nonlocal conservation laws Nonlocal boundary value problemHyperbolic partial differential equationAnalysisdescription
Abstract 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-09-11 |