Existence of secondary bifurcations or isolas for PDEs

Author(s)

Gameiro, Marcio ^{[1, 2]} ; Lessard, Jean-Philippe ^{[3, 4]}

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat Computacao, BR-13560970 Sao Carlos, SP - Brazil

^[2] Kyoto Univ, Dept Math, Kyoto 6068502 - Japan

^[3] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 - USA

^[4] BCAM Basque Ctr Appl Math, Derio 48160, Bizkaia - Spain

• Document type: Journal article
• Source: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 74, n. 12, p. 4131-4137, AUG 2011.
• Web of Science Citations: 1

Abstract

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. (AU)

• FAPESP's process: 10/00875-9 - Topological methods and rigorous numerics for bifurcations of dynamical systems
• Grantee: Marcio Fuzeto Gameiro
• Support Opportunities: Regular Research Grants