Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials

TL;DR

This paper establishes the well-posedness and regularity of a Cahn-Hilliard system with dynamic boundary conditions and singular potentials, ensuring existence, uniqueness, and continuous dependence of solutions.

Contribution

It introduces a general framework for analyzing Cahn-Hilliard equations with dynamic boundary conditions and singular potentials, proving existence and regularity of solutions.

Findings

Existence of weak solutions with conservation of total mass

Continuous dependence of solutions on initial data

Additional regularity results for strong solutions

Abstract

The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn-Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a suitable setting for the conservation of a total mass in the bulk plus the boundary. A very general class of double-well like potentials is allowed. Moreover, some further regularity is obtained to guarantee the strong solution.