Symmetry and Bifurcation of Periodic Solutions in Neumann Boundary Value Problems
نویسندگان
چکیده
We consider a reaction-diffusion equation with Neumann boundary conditions and show that solutions to this problem may be obtained from a problem with periodic boundary conditions and equivariant under O(2) symmetry. We describe the solutions for Hopf bifurcation and mode interactions involving Hopf bifurcation, namely, steadystate/Hopf and Hopf/Hopf. Neumann boundary conditions constrain the solutions to fixed-point spaces of the original symmetry group. This allows us to describe branching and stability in the original problem by looking at previously studied problems with smaller isotropy. We also establish conditions under which solutions to problems with Neumann boundary conditions can be related to those of problems with Dirichlet boundary conditions.
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