Archive for Rational Mechanics and Analysis
, Volume 99, Issue 4, pp 301328
First online:
Stability and folds
 J. H. MaddocksAffiliated withDepartment of Mathematics, University of Maryland
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It is known that when one branch of a simple fold in a bifurcation diagram represents (linearly) stable solutions, the other branch represents unstable solutions. The theory developed here can predict instability of some branches close to folds, without knowledge of stability of the adjacent branch, provided that the underlying problem has a variational structure. First, one particular bifurcation diagram is identified as playing a special role, the relevant diagram being specified by the choice of functional plotted as ordinate. The results are then stated in terms of the shape of the solution branch in this distinguished bifurcation diagram. In many problems arising in elasticity the preferred bifurcation diagram is the loaddisplacement graph. The theory is particularly useful in applications where a solution branch has a succession of folds.
The theory is illustrated with applications to simple models of thermal selfignition and of a chemical reactor, both of which systems are of ÉmdenFowler type. An analysis concerning an elastic rod is also presented.
 Title
 Stability and folds
 Journal

Archive for Rational Mechanics and Analysis
Volume 99, Issue 4 , pp 301328
 Cover Date
 198712
 DOI
 10.1007/BF00282049
 Print ISSN
 00039527
 Online ISSN
 14320673
 Publisher
 SpringerVerlag
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 Authors

 J. H. Maddocks ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of Maryland, College Park