Well-posedness of a structured population model in spaces of measures

Structured population models are partial differential equations used for, e.g., describing the evolution of cell, animal or human populations with respect to a specific structuring variable. Such models are classically studied in the space of Lebesgue integrable functions. However, in this setting, we might deal with non-existence of a (global) solution or emergence of singularities. An idea to solve these problems is to formulate the model in measures. We will introduce the general setting and present an existence result for a type of structured population models derived in the book “Spaces of Measures and their Applications to Structured Population Models” from Düll, Gwiazda, Marciniak-Czochra and Skrzeczkowski. In the end, we will look at a specific structured population model describing leukemia to show how it works in practice.