Communications in Mathematical Sciences
Volume 13 (2015)
Hyperbolic predators vs. parabolic prey
Pages: 369 – 400
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.
nonlocal conservation laws, predatory-prey systems, mixed hyperbolic-parabolic problems
2010 Mathematics Subject Classification
35L65, 35M30, 92D25