Coupled stationary bifurcations in non-flux boundary value problems

Hans Armbruster, G. Dangelmayr

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

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 C2of 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.

Original languageEnglish (US)
Pages (from-to)167-192
Number of pages26
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume101
Issue number1
DOIs
StatePublished - 1987
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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