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.Comment: 35 pages, 7 figure
