Existence of secondary bifurcations or isolas for PDEs

In this paper, we introduce a method to conclude about the existence of secondary bifurcations or isolas of steady state solutions for parameter dependent nonlinear partial differential equations. The technique combines the Global Bifurcation Theorem, knowledge about the non-existence of nontrivial...

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Detalles Bibliográficos
Autores: Gameiro, M., Lessard, J.-P.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2011
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/632
Acceso en línea:http://hdl.handle.net/20.500.11824/632
Access Level:acceso abierto
Palabra clave:Bifurcations of equilibria for PDEs
Global Bifurcation Theorem
Rigorous numerics
Secondary bifurcation
Descripción
Sumario:In this paper, we introduce a method to conclude about the existence of secondary bifurcations or isolas of steady state solutions for parameter dependent nonlinear partial differential equations. The technique combines the Global Bifurcation Theorem, knowledge about the non-existence of nontrivial steady state solutions at the zero parameter value and explicit information about the coexistence of multiple nontrivial steady states at a positive parameter value. We apply the method to the two-dimensional SwiftHohenberg equation.