Coupled stationary bifurcations in non-flux boundary value problems

Hans Armbruster, G. Dangelmayr

Research output: Contribution to journalArticle

49 Citations (Scopus)

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

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Bifurcation
Boundary Value Problem
Lyapunov-Schmidt Reduction
Nonlinear Operator Equations
Bifurcation Theory
Bifurcation Diagram
Unfolding
Symmetry Group
Imperfect
Codimension
Unstable
Boundary conditions
Interval
Framework

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Coupled stationary bifurcations in non-flux boundary value problems. / Armbruster, Hans; Dangelmayr, G.

In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 101, No. 1, 1987, p. 167-192.

Research output: Contribution to journalArticle

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