We present a nonlinear predator-prey system consisting of a nonlocal conservation law for predators coupled with a parabolic equation for prey. The drift term in the predators' equation is a nonlocal function of the prey density, so that the movement of the predators can be directed towards regions with high prey density. Moreover, Lotka-Volterra type right hand sides describe the feeding. A theorem ensuring existence, uniqueness, continuous dependence of weak solutions, and various stability estimates is proved, in any space dimension. Numerical integrations show a few qualitative features of the solutions.
Hyperbolic predators vs. parabolic prey / Colombo, Rm; Rossi, E. - In: COMMUNICATIONS IN MATHEMATICAL SCIENCES. - ISSN 1539-6746. - 13:2(2015), pp. 369-400. [10.4310/CMS.2015.v13.n2.a6]
Hyperbolic predators vs. parabolic prey
Rossi E
2015
Abstract
We present a nonlinear predator-prey system consisting of a nonlocal conservation law for predators coupled with a parabolic equation for prey. The drift term in the predators' equation is a nonlocal function of the prey density, so that the movement of the predators can be directed towards regions with high prey density. Moreover, Lotka-Volterra type right hand sides describe the feeding. A theorem ensuring existence, uniqueness, continuous dependence of weak solutions, and various stability estimates is proved, in any space dimension. Numerical integrations show a few qualitative features of the solutions.Pubblicazioni consigliate
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