Spaces of Measures and their Applications to Structured Population Models

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.