Del 36 - Cambridge Monographs on Applied and Computational Mathematics

Spaces of Measures and their Applications to Structured Population Models

Inbunden, Engelska, 2021

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

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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.

Produktinformation

Utgivningsdatum2021-10-07
Mått158 x 235 x 25 mm
Vikt640 g
FormatInbunden
SpråkEngelska
SerieCambridge Monographs on Applied and Computational Mathematics
Antal sidor322
FörlagCambridge University Press
ISBN9781316519103

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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 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 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 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.

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.