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Author: Hömberg, Dietmar × Subject: weak-strong uniqueness ×

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Now showing 1 - 2 of 2
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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.
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    Weak entropy solutions to a model in induction hardening, existence and weak-strong uniqueness
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Hömberg, Dietmar; Lasarzik, Robert
    In this paper, we investigate a model describing induction hardening of steel. The related system consists of an energy balance, an ODE for the different phases of steel, and Maxwell's equations in a potential formulation. The existence of weak entropy solutions is shown by a suitable regularization and discretization technique. Moreover, we prove the weak-strong uniqueness of these solutions, i.e., that a weak entropy solutions coincides with a classical solution emanating form the same initial data as long as the classical one exists. The weak entropy solution concept has advantages in comparison to the previously introduced weak solutions, e.g., it allows to include free energy functions with low regularity properties corresponding to phase transitions.