Well-posedness and global attractors for a non-isothermal viscous relaxation of nonlocal Cahn-Hilliard equations

TL;DR

This paper studies the mathematical properties of a non-isothermal, viscous relaxation model for nonlocal Cahn-Hilliard equations, demonstrating well-posedness and the existence of global attractors with enhanced regularity.

Contribution

It establishes well-posedness and the existence of compact global attractors for a non-isothermal viscous nonlocal Cahn-Hilliard model, extending understanding of its long-term behavior.

Findings

Solution operators exhibit dissipation and conservation properties.

Existence of a family of compact global attractors.

Attractors are bounded in a more regular phase-space.

Abstract

We investigate a non-isothermal viscous relaxation of some nonlocal Cahn-Hilliard equations. This perturbation problem generates a family of solution operators, exhibiting dissipation and conservation. The solution operators admit a family of compact global attractors that are bounded in a more regular phase-space.