Structured Population Models on Polish Spaces: A unified approach including Graphs, Riemannian Manifolds and Measure Spaces

Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra, Jakub Skrzeczkowski

Published 2023-07-20Version 1

We provide well-posedness theory of a nonlinear structured population model on an abstract metric space which is only assumed to be separable and complete. To this end, we leverage the structure of the space of nonnegative Radon measures under the dual bounded Lipschitz distance (flat metric) which can be seen as a generalization of Wasserstein distance to nonconservative problems. Motivated by applications, the formulation of models on fairly general metric spaces allows us to consider processes on infinite-dimensional state spaces or on graphs combining discrete and continuous structures.