Computer-assisted equilibrium validation for the diblock copolymer model

DOI10.3934/dcds.2017045zbMath1364.35116OpenAlexW2557660592MaRDI QIDQ501487

Thomas Wanner

Publication date: 9 January 2017

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2017045

zbMATH Keywords

bifurcationphase field modelnumerical continuationcomputer-assisted proofmodified Cahn-Hilliard equationdiblock copolymers

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Nonlinear parabolic equations (35K55) Large deviations (60F10) Phase transformations in solids (74N99) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Higher-order parabolic equations (35K25)

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Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation ⋮ Computer-assisted bifurcation diagram validation and applications in materials science ⋮ Rigorous continuation of bifurcation points in the diblock copolymer equation ⋮ Computer-Assisted Proof of Heteroclinic Connections in the One-Dimensional Ohta--Kawasaki Model ⋮ Equilibrium validation for triblock copolymers via inverse norm bounds for fourth-order elliptic operators ⋮ Some improvements of invertibility verifications for second-order linear elliptic operators ⋮ Validation of the bifurcation diagram in the 2D Ohta–Kawasaki problem ⋮ Validated numerics for continuation and bifurcation of connecting orbits of maps ⋮ Cyclic symmetry induced pitchfork bifurcations in the diblock copolymer model ⋮ A computer‐assisted method for the diblock copolymer model ⋮ Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity ⋮ Rigorously Computing Symmetric Stationary States of the Ohta--Kawasaki Problem in Three Dimensions ⋮ Equilibrium validation in models for pattern formation based on Sobolev embeddings ⋮ Degenerate Nucleation in the Cahn--Hilliard--Cook Model ⋮ Validated Saddle-Node Bifurcations and Applications to Lattice Dynamical Systems ⋮ Optimal periodic structures with general space group symmetries in the Ohta-Kawasaki problem

Uses Software

• AUTO
• INTLAB

Cites Work

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