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Coupled stationary bifurcations in non-flux boundary value problems

Published online by Cambridge University Press:  24 October 2008

D. Armbruster  and
G. Dangelmayr
D. Armbruster
Affiliation:
Institute for Information Sciences, University of Tübingen, West Germany
G. Dangelmayr
Affiliation:
Institute for Information Sciences, University of Tübingen, West Germany
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Abstract

Coupled stationary bifurcations in nonlinear operator equations for functions, which are defined on a real interval with non-flux boundary conditions at the ends, are analysed in the framework of imperfect bifurcation theory. The bifurcation equations resulting from a Lyapunov–Schmidt reduction possess a natural structure which can be obtained by taking real parts of a diagonal action in ℂ2 of the symmetry group 0(2). A complete unfolding theory is developed and bifurcation equations are classified up to codimension two. Structurally stable bifurcation diagrams are given and their dependence on the wave numbers of the unstable modes is clarified.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 1 , January 1987 , pp. 167 - 192
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

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