UNSPECIFIED. (1991) BOUNDARY-CONDITIONS AS SYMMETRY CONSTRAINTS. LECTURE NOTES IN MATHEMATICS, 1463 . pp. 63-79. ISSN 0075-8434

Abstract

Fujii, Mimura, and Nishiura [1985] and Armbruster and Dangelmayr [1986, 1987] have observed that reaction-diffusion equations on the interval with Neumann boundary conditions can be viewed as restrictions of similar problems with periodic boundary conditions; and that this extension reveals the presence of additional symmetry constraints which affect the generic bifurcation phenomena. We show that, more generally, similar observations hold for multi-dimensional rectangular domains with either Neumann or Dirichlet boundary conditions, and analyse the group-theoretic restrictions that this structure imposes upon bifurcations. We discuss a number of examples of these phenomena that arise in applications, including the Taylor-Couette experiment, Rayleigh-Benard convection, and the Faraday experiment.

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