Cahn-Hilliard approach to some degenerate parabolic equations with dynamic boundary conditions

TL;DR

This paper establishes the existence of weak solutions for a class of degenerate parabolic equations with dynamic boundary conditions, using a Cahn-Hilliard framework and maximal monotone graph techniques.

Contribution

It introduces a novel approach to handle degenerate parabolic equations with dynamic boundary conditions via the Cahn-Hilliard system and maximal monotone graphs, broadening the class of solvable problems.

Findings

Proved existence of weak solutions for the considered equations.

Extended the applicability of the Cahn-Hilliard approach to degenerate parabolic equations.

Utilized maximal monotone graph methods to handle nonlinear terms.

Abstract

In this paper the well-posedness of some degenerate parabolic equations with a dynamic boundary condition is considered. To characterize the target degenerate parabolic equation from the Cahn-Hilliard system, the nonlinear term coming from the convex part of the double-well potential is chosen using a suitable maximal monotone graph. The main topic of this paper is the existence problem under an assumption for this maximal monotone graph for treating a wider class. The existence of a weak solution is proved.