The singular limit dynamics of semilinear damped wave equations

DOI10.1016/0022-0396(89)90065-XzbMath0699.35177OpenAlexW2027241373MaRDI QIDQ913130

Xavier Mora, Joan Solà-Morales

Publication date: 1989

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(89)90065-x

zbMATH Keywords

global attractorinvariant manifoldsemilinear damped wave equation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Second-order nonlinear hyperbolic equations (35L70)

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Large time behavior of a conserved phase-field system ⋮ Inertial manifolds of damped semilinear wave equations ⋮ Sufficient conditions for the continuity of inertial manifolds for singularly perturbed problems ⋮ Singularly perturbed 1D Cahn-Hilliard equation revisited ⋮ The singular limit dynamics of the phase-field equations ⋮ The Cahn–Hilliard equation as limit of a conserved phase-field system ⋮ Existence and continuity of inertial manifolds for the hyperbolic relaxation of the viscous Cahn-Hilliard equation ⋮ On convergent rate of the attractor for a singularly perturbed wave equation ⋮ The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension ⋮ Large time dynamics of a nonlinear spring-mass-damper model ⋮ Existence of fast traveling waves for some parabolic equations: A dynamical systems approach ⋮ An abstract approach to smoothness of invariant manifolds ⋮ Lower semicontinuity of the attractor for a singularly perturbed hyperbolic equation ⋮ Smoothness of the singular limit of inertial manifolds of singularly perturbed evolution equations ⋮ Scaling variables and asymptotic expansions in damped wave equations ⋮ Continuity of attractors ⋮ Approximation theories for inertial manifolds ⋮ Inertial Manifolds for Reaction Diffusion Equations in Higher Space Dimensions

Cites Work

• Invariant manifolds for flows in Banach spaces
• Regular attractors of semigroups and evolution equations
• Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations
• The Morse-Smale property for a semilinear parabolic equation
• Center manifolds and contractions on a scale of Banach spaces
• Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation
• Geometric theory of semilinear parabolic equations
• Finite-dimensional attracting manifolds in reaction-diffusion equations
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