Finite Dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono Equation in R^3

TL;DR

This paper proves that the global attractor for the hyperbolic Cahn-Hilliard-Oono equation in three-dimensional space has finite fractal dimension under natural conditions, extending previous work on its long-term behavior.

Contribution

It establishes the finite dimensionality of the global attractor for the hyperbolic Cahn-Hilliard-Oono equation in R^3 with sub-quintic non-linearity, advancing understanding of its asymptotic dynamics.

Findings

Finite fractal dimension of the global attractor in R^3.

Verification under natural assumptions on non-linearity and external force.

Extension of previous results to the hyperbolic relaxation case.

Abstract

In this paper, we continue the study of the hyperbolic relaxation of the Cahn-Hilliard-Oono equation with the sub-quintic non-linearity in the whole space $\R^3$ started in our previous paper and verify that under the natural assumptions on the non-linearity and the external force, the fractal dimension of the associated global attractor in the natural energy space is finite.