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Instabilities in chemically reacting mixtures

Cohen, Donald S. (1976) Instabilities in chemically reacting mixtures. Rocky Mountain Journal of Mathematics, 6 (4). pp. 551-560. ISSN 0035-7596. 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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1216/rmj-1976-6-4-551DOIArticle
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.
Funders:
Funding AgencyGrant Number
Army Research Office (ARO)DAHC-04-68-C-0006
NSFGP-32157X2
Issue or Number:4
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:13 Jan 2020 23:40

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