Local Bifurcations of Invariant Manifolds of the Cahn–Hilliard–Oono Equation

Our aim is to examine a periodic boundary value problem for the Cahn–Hilliard–Oono equation. This equation appeared as one of the possible modifications of the well-known Cahn–Hilliard equation. This modification is designed to assume additional factors in modeling physical and physicochemical proce...

Full description

Saved in:
Bibliographic Details
Published in:Lobachevskii journal of mathematics 2023-03, Vol.44 (3), p.1003-1017
Main Authors: Kulikov, A. N., Kulikov, D. A.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Bifurcations
Boundary value problems
Canonical forms
Geometry
Invariants
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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:Our aim is to examine a periodic boundary value problem for the Cahn–Hilliard–Oono equation. This equation appeared as one of the possible modifications of the well-known Cahn–Hilliard equation. This modification is designed to assume additional factors in modeling physical and physicochemical processes. The local bifurcations that arise when the stability is changed by spatially homogeneous solutions of the corresponding boundary value problem are studied for all possible variants of stability change, including cases of codimension 2. A special version of the equation is also considered, which leads to the possibility of bifurcations of two-dimensional local attractors formed by Lyapunov unstable solutions that are periodic in the evolutionary variable. The analysis of the problem is based on the use and development of such methods of the theory of infinite-dimensional dynamical systems as the methods of integral (invariant) manifolds and normal forms.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080223030174