Mathematical Aspects of Reacting and Diffusing Systems

  • Paul C. Fife

Part of the Lecture Notes in Biomathematics book series (LNBM, volume 28)

Table of contents

  1. Front Matter
    Pages I-IV
  2. Paul C. Fife
    Pages 1-3
  3. Paul C. Fife
    Pages 4-52
  4. Paul C. Fife
    Pages 73-83
  5. Paul C. Fife
    Pages 84-123
  6. Paul C. Fife
    Pages 124-133
  7. Paul C. Fife
    Pages 134-142
  8. Paul C. Fife
    Pages 143-154
  9. Paul C. Fife
    Pages 163-167
  10. Back Matter
    Pages 168-188

About this book

Introduction

Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R. Aris (1975), who himself was one of the main contributors to the theory. Enthusiasm for the models developed has been shared by parts of the mathematical community, and these models have, in fact, provided motivation for some beautiful mathematical results. There are analogies between chemical reactors and certain biological systems. One such analogy is rather obvious: a single living organism is a dynamic structure built of molecules and ions, many of which react and diffuse. Other analogies are less obvious; for example, the electric potential of a membrane can diffuse like a chemical, and of course can interact with real chemical species (ions) which are transported through the membrane. These facts gave rise to Hodgkin's and Huxley's celebrated model for the propagation of nerve signals. On the level of populations, individuals interact and move about, and so it is not surprising that here, again, the simplest continuous space-time interaction-migration models have the same g- eral appearance as those for diffusing and reacting chemical systems.

Keywords

Derivative Diffusing Systems Diffusionsgleichung Nichtlineare Differentialgleichung Parabolische Differentialgleichung Population differential equation

Authors and affiliations

  • Paul C. Fife
    • 1
  1. 1.Mathematics DepartmentUniversity of ArizonaTucsonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-93111-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1979
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-09117-2
  • Online ISBN 978-3-642-93111-6
  • Series Print ISSN 0341-633X
  • About this book