Lecture Notes on Mathematical Modelling in the Life Sciences

Parabolic Equations in Biology

Growth, reaction, movement and diffusion

Authors: Perthame, Benoit

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  • 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
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eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-319-19500-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $60.00
price for USA in USD
  • ISBN 978-3-319-19499-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

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.

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)


Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-319-19500-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $60.00
price for USA in USD
  • ISBN 978-3-319-19499-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Parabolic Equations in Biology
Book Subtitle
Growth, reaction, movement and diffusion
Authors
Series Title
Lecture Notes on Mathematical Modelling in the Life Sciences
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-19500-1
DOI
10.1007/978-3-319-19500-1
Softcover ISBN
978-3-319-19499-8
Series ISSN
2193-4789
Edition Number
1
Number of Pages
XII, 199
Number of Illustrations
26 b/w illustrations, 13 illustrations in colour
Topics