Reaction-Diffusion Equations

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This unique volume provides a valuable overview on the current state of work in the rapidly developing field of reaction-diffusion equations. Some of the articles survey particular applications such as in combustion theory, electrochemistry, and neurobiology. Other papers focus on the analytic behavior of reaction-diffusion equations such as blow-up, the formation of patterns, travelling wave solutions, and the Conley index. The contributors are internationally respected experts in their respective fields.

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Editorial Reviews

Ten articles survey both the wide range of situations in which reaction-diffusion equations can be usefully applied, such as biology (nerve propagation), electrochemistry, combustion (ignition), and ecology; and the equally wide range of classical partial differential equation techniques being brought to bear on such problems, such as comparison principles, nonlinear functional analysis, and topological index theory. No index. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780198533788
  • Publisher: Oxford University Press, USA
  • Publication date: 10/28/1990
  • Series: Oxford Science Publications
  • Pages: 240
  • Product dimensions: 6.38 (w) x 9.50 (h) x 0.75 (d)

Meet the Author

both at Heriot-Watt University
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Table of Contents

1. Blowup for Some Reactive-Euler Induction Models, J. Bebernes and A. Bressan
2. A New Scaling of a Problem in Combustion Theory, G.C. Wake et al.
3. Patterns, Waves and Interfaces in Excitable Reaction-Diffusion Systems, M. Mimura
4. Reduced Equivariant Conley Index and Applications, J. Smoller and A. Wasserman
5. Remarks on the Equilibrium Theory for the Cahn-Hilliard Equation in One Space Dimension, N.D. Alikakos and W.R. McKinney
6. Excitability Behaviour of Myelinated Axon Models, J. Bell
7. Eigenvalue Problems with Indefinite Weights and Reaction-Diffusion Models in Population Dynamics, C. Cosner
8. Mathematical Aspects of Electrophoresis, P.C. Fife and X. Geng
9. Topological Methods for the Study of Travelling Wave Solutions of Reaction-Diffusion Systems, R.A. Gardner
10. Maximum Principles and Decoupling for Positive Solutions of Reaction-Diffusion Systems, J. Hernandez

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