On the existence of generalized solutions to a spatio-temporal predator-prey system
- Hömberg, Dietmar
- Lasarzik, Robert
- Plato, Luisa
2020 Mathematics Subject Classification
- 35D99 35Q92 35K51 35K55
- Generalized solution, nonlinear coupled PDEs, weak-strong uniqueness
In this paper we consider a pair of coupled non-linear partial differential equations describing the interaction of a predator-prey pair. We introduce a concept of generalized solutions and show the existence of such solutions in all space dimension with the aid of a regularizing term, that is motivated by overcrowding phenomena. 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.