Boundary conditions as symmetry constraints
- Cite this paper as:
- Crawford J.D., Golubitsky M., Gomes M.G.M., Knobloch E., Stewart I.N. (1991) Boundary conditions as symmetry constraints. In: Roberts M., Stewart I. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1463. Springer, Berlin, Heidelberg
Fujii, Mimura, and Nishiura  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 additonal 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-Bénard convection, and the Faraday experiment.
Unable to display preview. Download preview PDF.