Invariant Manifolds. Global Attractor of a Generalized Version of the Nonlocal Ginzburg–Landau Equation

We consider a generalized nonlocal Ginzburg–Landau equation with periodic boundary conditions. For the corresponding initial-boundary value problem we prove the existence of a solution for all positive values of the evolution variable. We study the existence and properties of invariant manifolds. We...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-03, Vol.270 (5), p.693-713
Main Authors: Kulikov, A. N., Kulikov, D. A.
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Euclidean geometry
Initial conditions
Invariants
Landau-Ginzburg equations
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
Orbital stability
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider a generalized nonlocal Ginzburg–Landau equation with periodic boundary conditions. For the corresponding initial-boundary value problem we prove the existence of a solution for all positive values of the evolution variable. We study the existence and properties of invariant manifolds. We extract a class of invariant manifolds the union of which forms a global attractor. We describe the structure of the attractor and find the Euclidean dimension of its components. In the metric of the space of initial conditions, we also study the Lyapunov stability and orbital stability of solutions that belong in the global attractor.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06381-6