Cohen, Donald S. (1976) Instabilities in chemically reacting mixtures. Rocky Mountain Journal of Mathematics, 6 (4). pp. 551-560. ISSN 0035-7596. doi:10.1216/rmj-1976-6-4-551. https://resolver.caltech.edu/CaltechAUTHORS:20200113-144056254
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Abstract
We shall study two different types of instability which arise in the theory of chemical and biochemical reactions [1], [2] and in the study of heat and mass transfer in porous catalysts [3], [4]. Peculiar physical effects involving local regions of oscillation and local instability (in a sense to be explained below) are observed experimentally. For each of the two different types of phenomena we believe that we have identified one possible mechanism for such occurrences. In § 2 we shall show that the sudden transition to localized temporal oscillation is reflected in a special situation first observed by N. Levinson [5]. The underlying chemistry and mathematics is introduced via a very simple initial value problem for a model system of reaction equations. A singular perturbation analysis clearly reveals the structure of the solution and also the mechanism which governs the occurrence of the oscillatory instabilities. In § 3 we consider the phenomenon of localized steady spatial oscillation for general reaction-diffusion equations. By combining singular perturbation and generalized WKB type methods we present a general technique for studying this type of phenomenon.
Item Type: | Article | ||||||
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Additional Information: | © 1976 Rocky Mountain Mathematics Consortium. This work was partially supported by the U.S. Army Research Office under Contract DAHC-04-68-C-0006 and the National Science Foundation under Grant GP-32157X2. | ||||||
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Issue or Number: | 4 | ||||||
DOI: | 10.1216/rmj-1976-6-4-551 | ||||||
Record Number: | CaltechAUTHORS:20200113-144056254 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200113-144056254 | ||||||
Official Citation: | Cohen, Donald S. Instabilities in chemically reacting mixtures. Rocky Mountain J. Math. 6 (1976), no. 4, 551--560. doi:10.1216/RMJ-1976-6-4-551. https://projecteuclid.org/euclid.rmjm/1250130120 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 100691 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | Tony Diaz | ||||||
Deposited On: | 13 Jan 2020 23:40 | ||||||
Last Modified: | 16 Nov 2021 17:56 |
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