WIAS Preprint No. 2925, (2022)

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


  • Hömberg, Dietmar
    ORCID: 0000-0001-9460-5729
  • Lasarzik, Robert
    ORCID: 0000-0002-1677-6925
  • Plato, Luisa
    ORCID: 0000-0003-3456-1570

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.

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