Hyperbolic predators vs parabolic preys
Analysis of PDEs
2014-02-11 v1
Abstract
We present a nonlinear predator-prey system consisting of a nonlocal conservation law for predators coupled with a parabolic equation for preys. The drift term in the predators' equation is a nonlocal function of the prey density, so that the movement of predators can be directed towards region 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.
Cite
@article{arxiv.1402.2099,
title = {Hyperbolic predators vs parabolic preys},
author = {Rinaldo M. Colombo and Elena Rossi},
journal= {arXiv preprint arXiv:1402.2099},
year = {2014}
}
Comments
35 pages, 7 figures