On the Swift-Hohenberg equation with slow and fast dynamics: well-posedness and long-time behavior

zbMath1331.35048MaRDI QIDQ905422

Andrea Giorgini

Publication date: 19 January 2016

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

zbMATH Keywords

global attractorexponential attractorsrobust family of exponential attractors

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Singular perturbations in context of PDEs (35B25) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26) Semilinear parabolic equations (35K58)

Related Items (8)

Dissipative mechanism and global attractor for modified Swift-Hohenberg equation in $R^{N}$ ⋮ Slow motion for the 1D Swift-Hohenberg equation ⋮ Regular dynamics of non-autonomous retarded Swift-Hohenberg equations ⋮ Exponential attractors for modified Swift-Hohenberg equation in \(\mathbb{R}^N\). ⋮ Rational spline-nonstandard finite difference scheme for the solution of time-fractional Swift-Hohenberg equation ⋮ Long-time dynamics of the Swift-Hohenberg equations ⋮ On the two dimensional fast phase transition equation: well-posedness and long-time dynamics ⋮ Analysis of a quasi-reversibility method for nonlinear parabolic equations with uncertainty data

Cites Work

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• Asymptotic dynamical difference between the nonlocal and local Swift–Hohenberg models
• Well-posedness and long-time behavior for the modified phase-field crystal equation
• Pattern Formation and Dynamics in Nonequilibrium Systems
• Exponential attractors for a nonlinear reaction-diffusion system in
• Some Canonical Bifurcations in the Swift–Hohenberg Equation
• Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems
• Attractors for semilinear strongly damped wave equations on \(\mathbb{R}^3\).
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