Bifurcations in the regularized Ericksen bar model

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dc.creatorGrinfeld, M.
dc.creatorLord, G. J.
dc.date2007-11-08
dc.date2008-01-17
dc.date.accessioned2026-07-07T08:54:45Z
dc.date.available2026-07-07T08:54:45Z
dc.descriptionWe consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation methods, the structure of bifurcations from double zero eigenvalues. Our results provide evidence in support of Müller's conjecture \cite{Muller} concerning the symmetry of local minimizers of the associated energy functional and describe in detail the structure of the primary branch connections that occur in this problem. We give a reformulation of Müller's conjecture and suggest two further conjectures based on the local analysis and numerical observations. We conclude by analysing a ``loop'' structure that characterizes $(k,3k)$ bifurcations.
dc.identifierhttps://arxiv.org/abs/0711.1257
dc.identifierhttp://arxiv.org/abs/0711.1257
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146048
dc.subjectDynamical Systems
dc.titleBifurcations in the regularized Ericksen bar model
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