Rigorous numerics for dissipative partial differential equations. II: Periodic orbit for the Kuramoto-Sivashinsky PDE -- a computer-assisted proof

DOI10.1007/s10208-002-0080-8zbMath1066.65105OpenAlexW2100375085MaRDI QIDQ1885383

Publication date: 28 October 2004

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10208-002-0080-8

zbMATH Keywords

Galerkin method a priori bounds differential inclusion periodic orbit Poincaré section Poincaré return map dissipative partial differential equation Lohner algorithm computer-assistent proof Kuramoto-Sivashinksy equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) A priori estimates in context of PDEs (35B45) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical nonlinear stabilities in dynamical systems (65P40)

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