Rigorous continuation of bifurcation points in the diblock copolymer equation

DOI10.3934/JCD.2017003zbMath1404.35030OpenAlexW2762201087MaRDI QIDQ1654464

Thomas Wanner, Jean-Philippe Lessard, Evelyn Sander

Publication date: 8 August 2018

Published in: Journal of Computational Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jcd.2017003

zbMATH Keywords

pitchfork bifurcationsbifurcation diagramsaddle-node bifurcationscomputer assisted-proofdiblock copolymer model

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Nonlinear parabolic equations (35K55) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Initial-boundary value problems for higher-order parabolic equations (35K35) Interval and finite arithmetic (65G30) Phase transformations in solids (74N99) Algorithms with automatic result verification (65G20) Bifurcations in context of PDEs (35B32) Numerical bifurcation problems (65P30) Group-invariant bifurcation theory in infinite-dimensional spaces (58E09)

Related Items (11)

Computer-assisted bifurcation diagram validation and applications in materials science ⋮ Equilibrium validation for triblock copolymers via inverse norm bounds for fourth-order elliptic operators ⋮ Cyclic symmetry induced pitchfork bifurcations in the diblock copolymer model ⋮ A Posteriori Validation of Generalized Polynomial Chaos Expansions ⋮ Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems ⋮ Rigorously Computing Symmetric Stationary States of the Ohta--Kawasaki Problem in Three Dimensions ⋮ Equilibrium validation in models for pattern formation based on Sobolev embeddings ⋮ From the Lagrange polygon to the figure eight. I: Numerical evidence extending a conjecture of Marchal ⋮ The Cahn-Hilliard equation with a nonlinear source term ⋮ Computer-Assisted Methods for Analyzing Periodic Orbits in Vibrating Gravitational Billiards ⋮ Rigorous Verification of Hopf Bifurcations via Desingularization and Continuation

Uses Software

• INTLAB
• CkAnalytic

Cites Work

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