Admissibly inertial manifolds for a class of semi-linear evolution equations

Consider the semi-linear evolution equation du(t)dt+Au(t)=f(t,u). We prove the existence of a new class of inertial manifolds called admissibly inertial manifolds for this equation. These manifolds are constituted by trajectories of the solutions belonging to rescaledly admissible function spaces wh...

Full description

Saved in:
Bibliographic Details
Published in:Journal of Differential Equations 2013-03, Vol.254 (6), p.2638-2660
Main Author: Nguyen, Thieu Huy
Format: Article
Language:English
Subjects:
Admissibility of function spaces
Admissibly inertial manifolds
Lyapunov–Perron method
Semilinear evolution equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Consider the semi-linear evolution equation du(t)dt+Au(t)=f(t,u). We prove the existence of a new class of inertial manifolds called admissibly inertial manifolds for this equation. These manifolds are constituted by trajectories of the solutions belonging to rescaledly admissible function spaces which contain wide classes of function spaces like weighted Lp-spaces, the Lorentz spaces Lp,q and many other rescaling function spaces occurring in interpolation theory. The existence of these manifolds is obtained in the case that the partial differential operator A is positive definite and self-adjoint with a discrete spectrum, and the nonlinear forcing term f satisfies the φ-Lipschitz conditions on the domain D(Aθ), 0⩽θ
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2013.01.001