A predator–prey system with L1 data

In this paper, we are concerned with a system of nonlinear partial differential equations modeling a predator–prey system in heterogeneous habitats. Preys are assumed to follow a logistic growth in the absence of predation, and predators are assumed to feed on preys with a Holling type II functional response to prey density. Also, interactions between predators are modelized by the statement of a food pyramid condition. Assuming no-flux boundary conditions and L1 data, we prove the existence of at least one weak solution.  2002 Elsevier Science (USA). All rights reserved.