Düll, Christian;
Gwiazda, Piotr;
Marciniak-Czochra, Anna;
Skrzeczkowski, Jakub
Structured population models on Polish spaces: A unified approach including graphs, Riemannian manifolds and measure spaces to describe dynamics of heterogeneous populations
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Medientyp:
E-Artikel
Titel:
Structured population models on Polish spaces: A unified approach including graphs, Riemannian manifolds and measure spaces to describe dynamics of heterogeneous populations
Beteiligte:
Düll, Christian;
Gwiazda, Piotr;
Marciniak-Czochra, Anna;
Skrzeczkowski, Jakub
Erschienen:
World Scientific Pub Co Pte Ltd, 2024
Erschienen in:Mathematical Models and Methods in Applied Sciences
Beschreibung:
<jats:p> This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes appear in a variety of applications, such as crowd dynamics, tissue regeneration, cancer development and coagulation-fragmentation processes. The diverse applications pose a common challenge to mathematicians due to the multiscale nature of the structures that underlie the system’s self-organization and control. Similar abstract mathematical problems arise when formulating problems in the language of measure evolution on a multi-faceted state space. Motivated by these observations, we propose a general mathematical framework for nonlinear structured population models on abstract metric spaces, which are only assumed to be separable and complete. We exploit the structure of the space of non-negative Radon measures with the dual bounded Lipschitz distance (flat metric), which is a generalization of the Wasserstein distance, capable of addressing non-conservative problems. The formulation of models on general metric spaces allows considering infinite-dimensional state spaces or graphs and coupling discrete and continuous state transitions. This opens up exciting possibilities for modeling single-cell data, crowd dynamics or coagulation-fragmentation processes. </jats:p>