Approximate inertial manifolds of Burgers equation approached by nonlinear Galerkin's procedure and its application

DOI10.1016/j.cnsns.2011.03.004zbMath1231.65171OpenAlexW1992139852MaRDI QIDQ654330

Jia-Zhong Zhang, Yan Liu, Pei-Hua Feng

Publication date: 28 December 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2011.03.004

zbMATH Keywords

numerical examplesnonlinear dynamicsnonlinear Galerkin methodBurgers equationglobal attractorshock wavemodel reductioninertial manifoldsdissipative dynamic systems

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) KdV equations (Korteweg-de Vries equations) (35Q53) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Dynamics and control of the 2-d Navier-Stokes equations ⋮ A geometric singular perturbation approach for planar stationary shock waves ⋮ Dynamics and control of the seven-mode truncation system of the 2-d Navier-Stokes equations ⋮ Optimal combination of spatial basis functions for the model reduction of nonlinear distributed parameter systems ⋮ Nonlinear Galerkin method for low-dimensional modeling of fluid dynamic system using POD modes ⋮ Fourier spectral approximation to global attractor for 2D convective Cahn-Hilliard equation ⋮ Formations of Transitional Zones in Shock Wave with Saddle-Node Bifurcations

Cites Work

• An approximate inertial manifold for computing Burgers' equation
• Model reduction on inertial manifolds for N-S equations approached by multilevel finite element method
• A nonlinear Galerkin method for the Navier-Stokes equations
• On approximate inertial manifolds to the Navier-Stokes equations
• Infinite-dimensional dynamical systems in mechanics and physics.
• Inertial manifolds with delay
• Chaotic dynamics of an unstable Burgers equation
• Dynamics and synchronization of numerical solutions of the Burgers equation
• Dynamics in spectral solutions of Burgers equation

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