Existence of secondary bifurcations or isolas for PDEs

DOI10.1016/J.NA.2011.03.046zbMath1221.35052OpenAlexW1985201401MaRDI QIDQ544176

Marcio Gameiro, Jean-Philippe Lessard

Publication date: 14 June 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11824/632

zbMATH Keywords

periodic boundary conditionstwo-dimensional Swift-Hohenberg equation

Mathematics Subject Classification ID

Abstract bifurcation theory involving nonlinear operators (47J15) Bifurcations in context of PDEs (35B32)

Related Items (1)

Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach

Cites Work

• Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs
• Validated continuation over large parameter ranges for equilibria of PDEs
• Global attractor of the Cahn-Hilliard equation in \(H^k\) spaces
• Numerical scheme for Swift-Hohenberg equation with strict implementation of Lyapunov functional.
• Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation
• Global attractor for a modified Swift-Hohenberg equation
• Rigorous computation of smooth branches of equilibria for the three dimensional Cahn-Hilliard equation
• Some global results for nonlinear eigenvalue problems
• Validated Continuation for Equilibria of PDEs
• Global smooth solution curves using rigorous branch following
• Chaotic Braided Solutions via Rigorous Numerics: Chaos in the Swift–Hohenberg Equation

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