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 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.