Analysis of a coupled pair of Cahn-Hilliard equations with nondegenerate mobility

Document Type : Research Article


Department of Mathematics, College of Sciences, University of Basrah, Basrah, Iraq


A mathematical analysis is performed for a system consisting of two coupled Cahn-Hilliard equations. These equations incorporate a diffusional mobility that depends on concentration. This modeling approach is often used to describe the process of phase separation in a thin layer of a binary liquid mixture covering a substrate, particularly when one of the components wets the substrate. The analysis establishes the existence of a weak formulation for this problem, which is supported by the use of a Lyapunov functional. Additionally, the analysis provides insights into the regularity properties of the weak formulation.


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