Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Time-averaged coarse variables for multi-scale dynamics


Authors: Marshall Slemrod and Amit Acharya
Journal: Quart. Appl. Math. 70 (2012), 793-803
MSC (2010): Primary 34E13; Secondary 34E15, 34C29, 35A35
DOI: https://doi.org/10.1090/S0033-569X-2012-01291-5
Published electronically: July 18, 2012
MathSciNet review: 3052092
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Abstract: Given an autonomous system of Ordinary Differential Equations without an a priori split into slow and fast components, we define a strategy for producing a large class of `slow' variables (constants of fast motion) in a precise sense. The equation of evolution of any such slow variable is deduced. The strategy is to rewrite our system on an infinite-dimensional ``history'' Hilbert space $ X$ and define our coarse observation as a functional on $ X$.


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Additional Information

Marshall Slemrod
Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
Email: slemrod@math.wisc.edu

Amit Acharya
Affiliation: Civil & Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvannia 15213
Email: acharyaamit@cmu.edu

DOI: https://doi.org/10.1090/S0033-569X-2012-01291-5
Received by editor(s): August 29, 2011
Published electronically: July 18, 2012
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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