Overview
- Provides the basic content for a course at master level on fundamental models in mathematics used for modeling in biology
- Includes applications to ecology and population dynamics, neurosciences, enzymatic reactions and chemotaxis
- Presents an original and rigorous presentation of several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations
Part of the book series: Lecture Notes on Mathematical Modelling in the Life Sciences (LMML)
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Table of contents (10 chapters)
Keywords
About this book
This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.
Reviews
“This book presents a variety of phenomena arising in the analysis of partial differential equations modelling of biological, physical and chemical processes. … This book can well serve as a textbook for a course on master's level. Exercise problems are given in each chapter.” (Jonathan Zinsl, zbMATH 1333.35001, 2016)
Authors and Affiliations
About the author
Benoit Perthame is presently a Professor at the University Pierre et Marie Curie where he heads the Laboratoire Jacques-Louis Lions. Before that he was a professor at Ecole Normale Supérieure in Paris where he begun to develop a research ideated to several aspects of mathematical biology: collective motion of cells, adaptation and evolution theory, modeling in tumor growth and therapy. Benoit Perthame was a plenary speaker at ICM Seoul, 2014.
Bibliographic Information
Book Title: Parabolic Equations in Biology
Book Subtitle: Growth, reaction, movement and diffusion
Authors: Benoît Perthame
Series Title: Lecture Notes on Mathematical Modelling in the Life Sciences
DOI: https://doi.org/10.1007/978-3-319-19500-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-19499-8Published: 17 September 2015
eBook ISBN: 978-3-319-19500-1Published: 09 September 2015
Series ISSN: 2193-4789
Series E-ISSN: 2193-4797
Edition Number: 1
Number of Pages: XII, 199
Number of Illustrations: 26 b/w illustrations, 13 illustrations in colour
Topics: Mathematical and Computational Biology, Applications of Mathematics