Boundary conditions as symmetry constraints

J.D. Crawford, M. Golubitsky, M.G.M. Gomes, E. Knobloch and I.N. Stewart
Boundary conditions as symmetry constraints
In: Singularity Theory and Its Applications, Warwick 1989, Part II. (M. Roberts and I.N. Stewart, eds.) Lecture Notes in Math. 1463 Springer-Verlag, Heidelberg, 1991, 63-79.

Abstract

Fujii, Minmura, 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 eigher 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.

J.D. Crawford, M. Golubitsky, M.G.M. Gomes, E. Knobloch and I.N. Stewart Boundary conditions as symmetry constraints In: Singularity Theory and Its Applications, Warwick 1989, Part II. (M. Roberts and I.N. Stewart, eds.) Lecture Notes in Math. 1463 Springer-Verlag, Heidelberg, 1991, 63-79.

Abstract

J.D. Crawford, M. Golubitsky, M.G.M. Gomes, E. Knobloch and I.N. Stewart
Boundary conditions as symmetry constraints
In: Singularity Theory and Its Applications, Warwick 1989, Part II. (M. Roberts and I.N. Stewart, eds.) Lecture Notes in Math. 1463 Springer-Verlag, Heidelberg, 1991, 63-79.