A mixed hyperbolic-parabolic system to describe predator-prey dynamics

Following [2], a model aiming at the description of two competing populations is introduced. In particular, it is considered a nonlinear system consisting of a nonlocal conservation law for predators coupled with a parabolic equation for prey. The drift term in the equation for predators is in general a nonlocal and nonlinear function of the prey density: the movement of predators can hence be directed towards regions where the concentration of prey is higher. Lotka-Volterra type right hand sides describe the feeding. In [2] the resulting Cauchy problemis proved to be well posed in any space dimension with respect to the L1 topology, and estimates on the growth of the solution in L1 and L∞norm and on the time dependence are provided. Numerical integrations show a few qualitative features of the solutions. This is a joint work with RinaldoM. Colombo.