Shadowing for discrete approximations of abstract parabolic equations

DOI10.3934/DCDSB.2008.10.19zbMath1158.65066OpenAlexW2324420703MaRDI QIDQ933172

Wolf-Jürgen Beyn, Serguei Piskarev

Publication date: 21 July 2008

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

Full work available at URL: https://doi.org/10.3934/dcdsb.2008.10.19

zbMATH Keywords

Banach spaceshadowingfinite-difference discretizationfinite-element discretizationabstract nonlinear parabolic problemsemi-discretization scheme

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Nonlinear differential equations in abstract spaces (34G20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical solutions to equations with nonlinear operators (65J15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Nonlinear evolution equations (47J35)

Related Items (8)

On approximation of coefficient inverse problems for differential equations in functional spaces ⋮ Approximations of Parabolic Equations at the Vicinity of Hyperbolic Equilibrium Point ⋮ Topological structural stability of partial differential equations on projected spaces ⋮ The exponential dichotomy on general approximation scheme ⋮ Approximation of semilinear fractional Cauchy problem. II ⋮ The exponential dichotomy under discretization on general approximation scheme ⋮ Dynamics of parabolic equations via the finite element method. I: Continuity of the set of equilibria. ⋮ Approximations of stable manifolds in the vicinity of hyperbolic equilibrium points for fractional differential equations

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