Admissible inertial manifolds for neutral equations and applications

• Published in: Dynamical 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
• Language: English
• Published: Taylor & Francis 02-10-2021
• Subjects: Admissible inertial manifolds; finite delay; heat transfer; Lyapunov-Perron method; materials with memory; neutral differential equations
• ISSN: 1468-9367; 1468-9375
• DOI: 10.1080/14689367.2021.1971623

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.