Admissible inertial manifolds for neutral equations and applications

We study the existence of admissible inertial manifolds for parabolic neutral functional differential equations of the form where the linear differential operator A is positive definite and self-adjoint with a discrete spectrum, the difference operator F is a bounded linear operator, and the delay n...

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Bibliographic Details
Published inDynamical systems (London, England) Vol. 36; no. 4; pp. 608 - 630
Main Authors Vu, Thi Ngoc Ha, Nguyen, Thieu Huy, Le, Anh Minh
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.10.2021
Taylor & Francis Ltd
Subjects
Admissible inertial manifolds
Differential equations
finite delay
Finite differences
Function space
heat transfer
Linear operators
Lyapunov-Perron method
Manifolds
materials with memory
Mathematical analysis
neutral differential equations
Operators (mathematics)
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Summary:We study the existence of admissible inertial manifolds for parabolic neutral functional differential equations of the form where the linear differential operator A is positive definite and self-adjoint with a discrete spectrum, the difference operator F is a bounded linear operator, and the delay nonlinear operator f is φ-Lipschitz for φ belonging to an admissible function space defined on . Our method is based on Lyapunov-Perron's equations, duality estimates in admissible spaces and F-induced trajectories. An application to heat transfer with delays in materials with memory is also given to illustrate our results.
ISSN:1468-9367
1468-9375
DOI:10.1080/14689367.2021.1971623