Spaces of Measures and their Applications to Structured Population Models

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

doi:10.1017/9781009004770

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Busse, Jan-Erik Cuadrado, Sílvia and Marciniak-Czochra, Anna 2022. Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation. Journal of Mathematical Biology, Vol. 84, Issue. 1-2,

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Franco, Eugenia Diekmann, Odo and Gyllenberg, Mats 2023. Modelling physiologically structured populations: renewal equations and partial differential equations. Journal of Evolution Equations, Vol. 23, Issue. 3,

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Martin, Hugo 2023. Measure framework for the pure selection equation: global well posedness and numerical investigations. MathematicS In Action, Vol. 12, Issue. 1, p. 155.

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Ackleh, Azmy S Lyons, Rainey and Saintier, Nicolas 2023. Finite difference schemes for a size structured coagulation-fragmentation model in the space of Radon measures. IMA Journal of Numerical Analysis, Vol. 43, Issue. 6, p. 3357.

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Ponce, Joan and Thieme, Horst R. 2023. Can infectious diseases eradicate host species? The effect of infection-age structure. Mathematical Biosciences and Engineering, Vol. 20, Issue. 10, p. 18717.

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Ackleh, Azmy S. Lyons, Rainey and Saintier, Nicolas 2023. High resolution finite difference schemes for a size structured coagulation-fragmentation model in the space of radon measures. Mathematical Biosciences and Engineering, Vol. 20, Issue. 7, p. 11805.

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Düll, Christian Gwiazda, Piotr Marciniak-Czochra, Anna and Skrzeczkowski, Jakub 2024. Structured population models on Polish spaces: A unified approach including graphs, Riemannian manifolds and measure spaces to describe dynamics of heterogeneous populations. Mathematical Models and Methods in Applied Sciences, Vol. 34, Issue. 01, p. 109.

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Christian Düll, Universität Heidelberg, Piotr Gwiazda, Polska Akademia Nauk (PAN), Warsaw, Anna Marciniak-Czochra, Universität Heidelberg, Jakub Skrzeczkowski, Uniwersytet Warszawski, Poland

Publisher:: Cambridge University Press
Online publication date:: September 2021
Print publication year:: 2021
Online ISBN:: 9781009004770
DOI:: https://doi.org/10.1017/9781009004770

Subjects:: Mathematics, Mathematical Biology, Computational Science, Differential and Integral Equations, Dynamical Systems and Control Theory
Series:: Cambridge Monographs on Applied and Computational Mathematics (36)

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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.

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Spaces of Measures and their Applications to Structured Population Models

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Notation
pp ix-xii

Introduction
pp 1-9

1 - Analytical Setting
pp 10-57

2 - Structured Population Models on the State Space R+
pp 58-99

3 - Structured Population Models on Proper Spaces
pp 100-147

4 - Numerical Methods for Structured Population Models
pp 148-185

5 - Recent Developments and Future Perspectives
pp 186-208

Appendix A - Topology, Compactness and Proper Spaces
pp 209-214

Appendix B - Functional Analysis
pp 215-219

Appendix C - Bounded Lipschitz and Hölder Functions
pp 220-228

Appendix D - Results on Approximation with Polynomials
pp 229-232

Appendix E - Differential Geometry
pp 233-234

Appendix F - Measure Theory
pp 235-241

Appendix G - Weaker Topologies on Spaces of Measure
pp 242-268

Appendix H - The Bochner Integral
pp 269-271

Appendix I - Semigroups
pp 272-277

Appendix J - Supplement to Chapter 2
pp 278-281

Appendix K - Technical Proofs from Chapter 3
pp 282-288

References
pp 289-306

Index
pp 307-308

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Spaces of Measures and their Applications to Structured Population Models

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