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Slowly modulated oscillations in nonlinear diffusion processes

Cohen, Donald S. and Hoppensteadt, Frank C. and Miura, Robert M. (1977) Slowly modulated oscillations in nonlinear diffusion processes. SIAM Journal on Applied Mathematics, 33 (2). pp. 217-229. ISSN 0036-1399. http://resolver.caltech.edu/CaltechAUTHORS:COHsiamjam77

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Abstract

It is shown here that certain systems of nonlinear (parabolic) reaction-diffusion equations have solutions which are approximated by oscillatory functions in the form R(ξ - cτ)P(t^*) where P(t^*) represents a sinusoidal oscillation on a fast time scale t* and R(ξ - cτ) represents a slowly-varying modulating amplitude on slow space (ξ) and slow time (τ) scales. Such solutions describe phenomena in chemical reactors, chemical and biological reactions, and in other media where a stable oscillation at each point (or site) undergoes a slow amplitude change due to diffusion.


Item Type:Article
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http://dx.doi.org/10.1137/0133013DOIUNSPECIFIED
Additional Information:© 1977 Society for Industrial and Applied Mathematics. Received by the editors February 11, 1976, and in revised form November 17, 1976. This work was performed at a workshop on Mathematical Problems in Ecology, August, 1975, organized by Professor Donald L. Ludwig, University of British Columbia, and supported by the National Research Council of Canada. [D.S.C. was] [s]upported in part by the U.S. Army Research Office under Contract DAHC-04-68-006 and the National Science Foundation under Grant GP32157X2. [F.C.H. was] [s]upported in part by the U.S. Air Force Scientific Research Office under Grant AFOSR-71-2107 and by the U.S. Army Research Office under Grant DAAG29-74-G-0219. [R.M.M. was] [s]upported in part by the National Science Foundation under Grant GP-34319. The authors gratefully acknowledge the hospitality of Professor Donald L. Ludwig, University of British Columbia, and that of the University of British Columbia.
Funders:
Funding AgencyGrant Number
Army Research OfficeDAHC-04-68-006
National Science FoundationGP32157X2
Air Force Scientific Research OfficeAFOSR-71- 2107
Army Research OfficeDAAG29-74-G-0219
National Science FoundationGP-34319
National Research Council of Canada (NRCC)UNSPECIFIED
Record Number:CaltechAUTHORS:COHsiamjam77
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:COHsiamjam77
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12658
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:18 Dec 2008 03:01
Last Modified:26 Dec 2012 10:38

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