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Rotating Spiral Waves and Oscillations in Reaction-Diffusion Equations

Cohen, Donald S. (1979) Rotating Spiral Waves and Oscillations in Reaction-Diffusion Equations. In: Applied Nonlinear Analysis: Proceedings of an International Conference on Applied Nonlinear Analysis. Academic Press , New York, NY, pp. 95-109. ISBN 978-0-12-434180-7. https://resolver.caltech.edu/CaltechAUTHORS:20200113-091053796

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Abstract

This chapter describes the rotating spiral waves and oscillations in reaction–diffusion equations. Rotating spiral waves arise naturally as models of spatially organized activity in various chemical and biochemical processes. The Belousov–Zhabotinsky reaction provides a classic example. Experiments with this reaction in a two-dimensional medium produce spiral concentration patterns that rotate with constant frequency about a fixed center. These waves result from interplay between the chemical process of reaction and the physical process of molecular diffusion. The chapter discusses the existence and various analytical and asymptotic properties of these waves. It presents the concrete computations for specific parameter values. The demonstration of the existence of such rotating spiral waves, which are smooth from the origin to infinity, resolves the important issue. The chapter explores the effect of spatial diffusion on oscillatory states in arbitrary multispecies growth models having hereditary terms.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/b978-0-12-434180-7.50014-0DOIArticle
Additional Information:© 1979 Academic Press, Inc. Supported in part by the U.S. Army Office under Contract DAHC-04-68-0006 and the National Science Foundation under Grant GP32157X2.
Funders:
Funding AgencyGrant Number
Army Research Office (ARO)DAHC-04-68-0006
NSFGP32157X2
Record Number:CaltechAUTHORS:20200113-091053796
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200113-091053796
Official Citation:Donald S. Cohen, ROTATING SPIRAL WAVES AND OSCILLATIONS IN REACTION-DIFFUSION EQUATIONS. Editor(s): V. Lakshmikantham, Applied Nonlinear Analysis, Academic Press, 1979, Pages 95-109, ISBN 9780124341807, https://doi.org/10.1016/B978-0-12-434180-7.50014-0. (http://www.sciencedirect.com/science/article/pii/B9780124341807500140)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100668
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Jan 2020 17:21
Last Modified:13 Jan 2020 17:21

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