Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system

TL;DR

This paper establishes the well-posedness and analyzes the long-term behavior of a novel nonstandard viscous Cahn-Hilliard system modeling phase transitions, ensuring solutions exist uniquely over time.

Contribution

It introduces a new viscous Cahn-Hilliard model with microforce and microenergy balances, proving existence, uniqueness, and describing the asymptotic behavior of solutions.

Findings

Existence and uniqueness of global smooth solutions

Boundedness properties of solutions

Description of the omega-limit set

Abstract

We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a careful development of uniform estimates and the deduction of certain useful boundedness properties, we prove existence and uniqueness of a global-in-time smooth solution to the associated initial/boundary-value problem; moreover, we give a description of the relative omega-limit set.