In this paper we deal with a doubly nonlinear Cahn–Hilliard system, where both an internal constraint on the time derivative of the concentration and a potential for the concentration are introduced. The definition of the chemical potential includes two regularizations: a viscous and a diffusive term. First of all, we prove existence and uniqueness of a bounded solution to the system using a nonstandard maximum-principle argument for time-discretizations of doubly nonlinear equations. Possibly including singular potentials, this novel result brings improvements over previous approaches to this problem. Secondly, under suitable assumptions on the data, we show the convergence of solutions to the respective limit problems once either of the two regularization parameters vanishes.

在本文中，我们处理一个双重非线性Cahn-Hilliard系统，其中引入了浓度时间导数的内部约束和浓度潜能。化学势的定义包括两个规则化：粘性和扩散项。首先，我们使用非标准的最大原理参数对双非线性方程组进行时间离散，证明了该系统有界解的存在性和唯一性。可能包括奇异的电势，这个新颖的结果带来了对该问题的以前方法的改进。其次，在适当的数据假设下，一旦两个正则化参数中的任何一个消失，我们就证明了相应极限问题解的收敛性。