Blowup in a Partial Differential Equation with Conserved First Integral
- Creators
- Budd, Chris
- Dold, Bill
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Stuart, Andrew
Abstract
A reaction-diffusion equation with a nonlocal term is studied. The nonlocal term acts to conserve the spatial integral of the unknown function as time evolves. Such equations give insight into biological and chemical problems where conservation properties predominate. The aim of the paper is to understand how the conservation property affects the nature of blowup. The equation studied has a trivial steady solution that is proved to be stable. Existence of nontrivial steady solutions is proved, and their instability established numerically. Blowup is proved for sufficiently large initial data by using a comparison principle in Fourier space. The nature of the blowup is investigated by a combination of asymptotic and numerical calculations.
Additional Information
© 1993 Society for Industrial and Applied Mathematics. Submitted: 25 September 1991. Accepted: 23 April 1992. The authors thank Professors J. T. Stuart and V. Galaktionov and Drs. M. Floater, A. Lacey, and Y. Tourigny for many helpful conversations.Attached Files
Published - 0153036.pdf
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Additional details
- Eprint ID
- 78143
- Resolver ID
- CaltechAUTHORS:20170613-080915743
- Created
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2017-06-13Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Other Numbering System Name
- Andrew Stuart
- Other Numbering System Identifier
- J23