Steady state bifurcations for the Kuramoto-Sivashinsky equation: a computer assisted proof

DOI10.3934/jcd.2015.2.95zbMath1326.35029OpenAlexW2525124707MaRDI QIDQ494285

Piotr Zgliczyński

Publication date: 31 August 2015

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

Full work available at URL: https://doi.org/10.3934/jcd.2015.2.95

zbMATH Keywords

periodic boundary conditionsdissipative PDEsmethod of self-consistent bounds

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10) Algorithms with automatic result verification (65G20) Bifurcations in context of PDEs (35B32)

Related Items (13)

Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation ⋮ Rigorous verification of saddle-node bifurcations in ODEs ⋮ Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity ⋮ Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems ⋮ Analysis and computations of a non-local thin-film model for two-fluid shear driven flows ⋮ A general framework for validated continuation of periodic orbits in systems of polynomial ODEs ⋮ Computer-assisted proofs of the existence of a symmetry-breaking bifurcation point for the Kolmogorov problem ⋮ Validated Saddle-Node Bifurcations and Applications to Lattice Dynamical Systems ⋮ Rigorous validation of a Hopf bifurcation in the Kuramoto-Sivashinsky PDE ⋮ Rigorous verification of Hopf bifurcations in functional differential equations of mixed type ⋮ Rigorous Verification of Hopf Bifurcations via Desingularization and Continuation ⋮ Finite element approximation of invariant manifolds by the parameterization method ⋮ Numerical Computations and Computer Assisted Proofs of Periodic Orbits of the Kuramoto--Sivashinsky Equation

Uses Software

• AUTO
• AUTO2000
• CAPD

Cites Work

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