Admissible inertial manifolds for infinite delay evolution equations
Bull. Korean Math. Soc. 2021 Vol. 58, No. 3, 669-688
Published online January 8, 2021
Printed May 31, 2021
Le Anh Minh
Hong Duc University
Abstract : The aim of this paper is to prove the existence of an admissible inertial manifold for mild solutions to infinite delay evolution equation of the form $$ \left \{ \begin{aligned} \frac{du}{dt}+Au & =F(t,u_t), \quad t\geq s, \medskip \\ u_s (\theta)&=\phi(\theta), \ \ \forall \theta \in ( -\infty, 0], \ \ s \in \R, \quad \end{aligned} \right. $$ where $A$ is positive definite and self-adjoint with a discrete spectrum, the Lipschitz coefficient of the nonlinear part $F$ may depend on time and belongs to some admissible function space defined on the whole line. The proof is based on the Lyapunov-Perron equation in combination with admissibility and duality estimates.
Keywords : Admissible inertial manifolds, admissible function spaces, infinite delay, Lyapunov-Perron method, Mackey-Glass, distributed delay
MSC numbers : Primary 34K30, 35B40, 35K58, 37L25
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