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

2016/08/29 by Fukao, Takeshi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.07913

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.

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