Admissible inertial manifolds for infinite delay evolution equations
Bull. Korean Math. Soc.
Published online January 8, 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
$$
\left \{
\begin{aligned}
\frac{du}{dt}+Au & =F(t,u_t),
\quad t\geq s,
\medskip
\\
u(s+\theta) & = u_s (\theta), \ \ \forall \theta \in ( -\infty, 0], \ \ s \in \R,
\quad
\end{aligned}
\right.
$$
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 : 34K30, 35B40, 35K58, 37L25
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