Invariant manifolds of admissible classes for semi-linear evolution equations

DOI10.1016/j.jde.2008.10.010zbMath1178.34070OpenAlexW2040348073MaRDI QIDQ1007258

Nguyen Thieu Huy

Publication date: 20 March 2009

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

Full work available at URL: https://doi.org/10.1016/j.jde.2008.10.010

zbMATH Keywords

integral equationsexponential dichotomyevolution equationsadmissibility of function spacesinvariant manifolds of admissible classeslocal-stable manifolds

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Invariant manifolds for ordinary differential equations (34C45)

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Cites Work

• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line
• Invariant manifolds of partial functional differential equations.
• Dynamics in infinite dimensions. Appendix by Krzysztof P. Rybakowski.
• Nonlinear semigroups and the existence and stability of solutions to semilinear nonautonomous evolution equations
• The spectral mapping theorem for evolution semigroups on spaces of vector-valued functions
• Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line
• One-Parameter Semigroups for Linear Evolution Equations
• Sufficient conditions for exponential stability and dichotomy of evolution equations
• Weak*-sequential closure and the characteristic of subspaces of conjugate Banach spaces
• Invariant manifolds
• Analytic semigroups and optimal regularity in parabolic problems
• Dynamics of evolutionary equations
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