Stable and unstable manifolds for hyperbolic bi-semigroups

DOI10.1016/j.jfa.2011.11.031zbMath1266.37039OpenAlexW1978658281MaRDI QIDQ765934

Mohamed Sami ElBialy

Publication date: 22 March 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2011.11.031

zbMATH Keywords

modulated wavessolitary wavesinvariant manifoldsRiccati equationsevolution equationselliptic equationsill-posed problemsexponential dichotomiesbi-semigroupsemigroup perturbations

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05)

Related Items (8)

Dichotomous solutions for semilinear ill-posed equations with sectorially dichotomous operator ⋮ A dynamical approach to semilinear elliptic equations ⋮ Continuous-time dichotomies without unstable invariant manifolds for autonomous system ⋮ Stable manifolds to bounded solutions in possibly ill-posed PDEs ⋮ A center manifold for second order semilinear differential equations on the real line and applications to the existence of wave trains for the Gurtin–McCamy equation ⋮ Stable and unstable manifolds for hyperbolic bi-semigroups ⋮ Existence and regularity of invariant graphs for cocycles in bundles: partial hyperbolicity case ⋮ GLOBAL STABLE AND UNSTABLE MANIFOLDS FOR A CLASS OF SEMILINEAR EQUATIONS WITH SECTORIALLY DICHOTOMOUS OPERATOR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Invariant manifolds for flows in Banach spaces
• The dynamical approach to elliptic problems in cylindrical domains, and a study of their parabolic singular limit
• Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on \(\mathbb R^2\)
• A smooth center manifold theorem which applies to some ill-posed partial differential equations with unbounded nonlinearities
• Stable and unstable manifolds for hyperbolic bi-semigroups
• The dichotomy theorem for evolution bi-families
• Locally Lipschitz perturbations of bisemigroups
• Semigroups of linear operators and applications to partial differential equations
• A reduction principle for nonautonomous systems in infinite-dimensional spaces
• Steady flows of inviscid fluids under localized perturbations
• Geometric theory of semilinear parabolic equations
• Stable and unstable manifolds for the nonlinear wave equation with dissipation
• On nonlinear problems of mixed type: A qualitative theory using infinite- dimensional center manifolds
• Robustness of exponential dichotomies in infinite-dimensional dynamical systems
• Essential manifolds for an elliptic problem in an infinite strip
• Invariant manifolds for parabolic partial differential equations on unbounded domains
• Invariant foliations for \(C^1\) semigroups in Banach spaces
• Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders
• The optimal gap condition for invariant manifolds
• Wave-solutions of reversible systems and applications
• A stable manifold theorem for degenerate fixed points with applications to celestial mechanics
• Global stability of vortex solutions of the two-dimensional Navier-Stokes equation
• On the Structure of Spectra of Modulated Travelling Waves
• Numerical Computation of Solitary Waves in Infinite Cylindrical Domains
• Dynamics of evolutionary equations

This page was built for publication: Stable and unstable manifolds for hyperbolic bi-semigroups