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.
- Includes appendices providing any necessary background material and collects results from various fields in one place
- Covers results concerning the functional analytic properties of spaces of measures, previously scattered over many papers using different notations
- Presents current trends and problems in the theory, allowing young researchers to jump quickly into research
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Product details
- Date Published: October 2021
- format: Hardback
- isbn: 9781316519103
- length: 300 pages
- dimensions: 235 x 158 x 25 mm
- weight: 0.64kg
- availability: Available
Table of Contents
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.
Look Inside
Authors
Christian Düll, Universität Heidelberg
Christian Düll is a member of the research team of Anna Marciniak-Czochra at Heidelberg University. He works with structured population models in a measure setting and optimal transport problems.
Piotr Gwiazda, Polska Akademia Nauk (PAN), Warsaw
Piotr Gwiazda is Professor at the Institute of Mathematics of the Polish Academy of Sciences and Head of the Department of Differential Equations. His fields of research include the topics of weak, renormalized and measure-valued solutions to nonlinear PDEs, with a focus on PDEs arising from fluid and solid mechanics as well as mathematical biology.
Anna Marciniak-Czochra, Universität Heidelberg
Anna Marciniak-Czochra is Professor of Applied Mathematics at Heidelberg University and Head of the research group 'Applied Analysis and Modelling in Biosciences' at the Institute of Applied Mathematics (IAM), Interdisciplinary Center of Scientific Computing (IWR) and BIOQUANT Center, Heidelberg University. She is the deputy director of the IAM and a member of the Board of the European Society for Theoretical and Mathematical Biology (ESMTB). Her interdisciplinary expertise lies in the areas of applied mathematics and mathematical and computational biosciences.
Jakub Skrzeczkowski, Uniwersytet Warszawski, Poland
Jakub Skrzeczkowski researches at the University of Warsaw under the supervision of Piotr Gwiazda. His work deals with measure solutions of structured population models, singular limits in reaction-diffusion systems and parabolic PDEs in a non-standard growth setting.