Spaces of Measures and their Applications to Structured Population Models

Presents a comprehensive analytical framework for structured population models in spaces of Radon measures and their numerical approximation.

Christian Düll (Author), Piotr Gwiazda (Author), Anna Marciniak-Czochra (Author), Jakub Skrzeczkowski (Author)

9781316519103, Cambridge University Press

Hardback, published 7 October 2021

300 pages
23.5 x 15.8 x 2.5 cm, 0.64 kg

Structured population models are transport-type equations often applied to describe evolution of heterogeneous populations of biological cells, animals or humans, including phenomena such as crowd dynamics or pedestrian flows. This book introduces the mathematical underpinnings of these applications, providing a comprehensive analytical framework for structured population models in spaces of Radon measures. The unified approach allows for the study of transport processes on structures that are not vector spaces (such as traffic flow on graphs) and enables the analysis of the numerical algorithms used in applications. Presenting a coherent account of over a decade of research in the area, the text includes appendices outlining the necessary background material and discusses current trends in the theory, enabling graduate students to jump quickly into research.

Notation
Introduction
1. Analytical setting
2. Structured population models on state space R+
3. Structured population models on proper spaces
4. Numerical methods for structured population models
5. Recent developments and future perspectives
Appendix A. Topology, compactness and proper spaces
Appendix B. Functional analysis
Appendix C. Bounded Lipschitz and Hölder functions
Appendix D. Results on approximation with polynomials
Appendix E. Differential geometry
Appendix F. Measure theory
Appendix G. Weaker topologies on spaces of measures
Appendix H. The Bochner integral
Appendix I. Semigroups
Appendix J. Supplement to Chapter 2
Appendix K. Technical proofs from Chapter 3
References
Index.

Subject Areas: Applied ecology [RNC], Mathematical modelling [PBWH], Probability & statistics [PBT], Differential calculus & equations [PBKJ]