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Author: Plato, Luisa × Subject: weak-strong uniqueness ×

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    On the existence of generalized solutions to a spatio-temporal predator-prey system
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Hömberg, Dietmar; Lasarzik, Robert; Plato, Luisa
    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.