analysis of a coupled pair of cahn-hilliard equations with nondegenerate mobility

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.