Lecture Notes in Biomathematics

Mathematical Aspects of Reacting and Diffusing Systems

Authors: Fife, P. C.

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About this book

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.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-642-93111-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-540-09117-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Aspects of Reacting and Diffusing Systems
Authors
Series Title
Lecture Notes in Biomathematics
Series Volume
28
Copyright
1979
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-93111-6
DOI
10.1007/978-3-642-93111-6
Softcover ISBN
978-3-540-09117-2
Series ISSN
0341-633X
Edition Number
1
Number of Pages
IV, 185
Topics