Analysis of the Cahn-Hilliard equation with a chemical potential dependent mobility
Maurizio Grasselli, Alain Miranville, Riccarda Rossi, Giulio, Schimperna
TL;DR
This paper investigates the mathematical properties of a generalized Cahn-Hilliard equation with a chemical potential-dependent mobility, focusing on well-posedness and the existence of global attractors.
Contribution
It extends the classical Cahn-Hilliard model by incorporating a chemical potential-dependent mobility and analyzes its well-posedness and long-term behavior.
Findings
Proved well-posedness of the generalized model
Established existence of global attractors
Extended understanding of phase separation dynamics
Abstract
The aim of this paper is to study the well-posedness and the existence of global attractors for a family of Cahn-Hilliard equations with a mobility depending on the chemical potential. Such models arise from generalizations of the (classical) Cahn-Hilliard equation due to M. E. Gurtin.
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Taxonomy
TopicsSolidification and crystal growth phenomena · Stability and Controllability of Differential Equations · Advanced Mathematical Modeling in Engineering