Bifurcation analysis to Swift-Hohenberg equation with perturbed boundary conditions. (English) Zbl 1221.37157

Ogawa, Toshiyuki; Okuda, Takashi

RIMS Kôkyûroku Bessatsu B3, 83-99 (2007).

The authors consider the Swift-Hohenberg equation with perturbed, in some special sense, boundary conditions. It is shown how the neutral stability curves change and, how the bifurcation diagrams change by the perturbation of the boundary conditions. The first result describes the neutral stability curves in the vicinity of the intersection point of two neutral stability curves, i.e. around multiple critical points, in the appropriate parameter space. Then, they apply the center manifold theory to study the local bifurcation structures around such critical point. Two main situations are shown.

Reviewer: Mariano Rodriguez Ricard (La Habana)

MSC:

37L10	Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems
35B32	Bifurcations in context of PDEs
35K30	Initial value problems for higher-order parabolic equations
35K55	Nonlinear parabolic equations

Keywords:

normal forms; center manifold theory; bifurcation