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 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 Swift-Hohenberg equation. (C) 2011 Elsevier Ltd. All rights reserved.

Japan Society for the Promotion of Science (JSPS)

JSPS[P08016]

JSPS[2008016]

Japan Society for the Promotion of Science (JSPS)

Ministry of Education, Culture, Sports, Science, and Technology of Japan

Ministry of Education, Science, Technology, Culture and Sports, Japan

Fapesp[Processo 2010/00875-9]

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CNPq[Processo 306453/2009-6]

NSF[DMS-0511115]

U.S. National Science Foundation (NSF)

DARPA

DARPA

U.S. Department of Energy (DOE)

US Department of Energy, Office of ScienceDOE[DE-FG02-05ER25711]