The initial boundary value problem for a Cahn–Hilliard system subject to a dynamic boundary condition of Allen–Cahn type is treated. The vanishing of the surface diffusion on the dynamic boundary condition is the point of emphasis. By the asymptotic analysis as the diffusion coefficient tends to 0, one can expect that the solutions of the surface diffusion problem converge to the solution of the problem without the surface diffusion. This is actually the case, but the solution of the limiting problem naturally looses some regularity. Indeed, the system we investigate is rather complicate due to the presence of nonlinear terms including general maximal monotone graphs both in the bulk and on the boundary. The two graphs are related each to the other by a growth condition, with the boundary graph that dominates the other one. In general, at the asymptotic limit a weaker form of the boundary condition is obtained, but in the case when the two graphs exhibit the same growth the boundary condition still holds almost everywhere.

讨论了具有Allen-Cahn型动态边界条件的Cahn-Hilliard系统的初始边值问题。在动态边界条件下表面扩散的消失是重点。通过随着扩散系数趋于0的渐近分析，可以期望表面扩散问题的解收敛到没有表面扩散的问题的解。确实是这种情况，但是限制问题的解决自然会失去一些规律性。的确，由于存在非线性项，包括整体和边界上的一般最大单调图，我们研究的系统相当复杂。这两个图通过增长条件相互关联，其中边界图主导另一个图。一般来说，