Parabolic Equations in Biology

Growth, reaction, movement and diffusion

  • Benoît Perthame

Table of contents

  1. Front Matter
    Pages i-xii
  2. Benoît Perthame
    Pages 1-21
  3. Benoît Perthame
    Pages 23-36
  4. Benoît Perthame
    Pages 57-85
  5. Benoît Perthame
    Pages 87-103
  6. Benoît Perthame
    Pages 105-116
  7. Benoît Perthame
    Pages 145-165
  8. Back Matter
    Pages 197-199

About this book

Introduction

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.

Keywords

Fokker-Planck equations Mathematical biology Reaction-diffusion Traveling waves Turing patterns

Authors and affiliations

  • Benoît Perthame
    • 1
  1. 1.LJLL, UPMCUniversité Pierre et Marie CurieParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-19500-1
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-19499-8
  • Online ISBN 978-3-319-19500-1
  • Series Print ISSN 2193-4789
  • Series Online ISSN 2193-4797
  • About this book
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