On the existence of generalized solutions to a spatio-temporal predator–prey system with prey-taxis

Abstract

In this paper we consider a pair of coupled nonlinear partial differential equations describing the interaction of a predator–prey pair including random movement as well as prey-taxis. We introduce a concept of generalized solutions and show the existence of such solutions in all space dimensions with the aid of a regularizing term. Additionally, we prove the weak–strong uniqueness of these generalized solutions and the existence of strong solutions at least locally in time for space dimension two and three.