Hyperbolic predators vs parabolic preys

Rinaldo M. Colombo; Elena Rossi

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arXiv · 1402.2099

Hyperbolic predators vs parabolic preys

Rinaldo M. Colombo·Elena Rossi

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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.

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Rinaldo M. Colombo, Elena Rossi. 2014-02-10. Hyperbolic predators vs parabolic preys. https://arxiv.org/abs/1402.2099

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