论文标题
Cahn-Hilliard方程的动态边界条件下的扩散消失
Vanishing diffusion in a dynamic boundary condition for the Cahn-Hilliard equation
论文作者
论文摘要
治疗了受艾伦-CAHN类型的动态边界条件的Cahn-Hilliard系统的初始边界值问题。在动态边界条件上表面扩散的消失是强调的点。通过渐近分析，由于扩散系数趋向于0，人们可以期望表面扩散问题的溶液在没有表面扩散的情况下会收敛到问题的溶液。实际上是这种情况，但是限制问题的解决方案自然会失去一些规律性。实际上，由于存在批量和边界中的一般最大单调图，包括一般最大单调图，我们研究的系统非常复杂。这两个图通过生长条件与彼此相关，而边界图则占据了另一个图。通常，在渐近极限下，获得了边界条件的较弱形式，但是在这两个图显示相同的生长的情况下，边界条件几乎在任何地方仍然存在。
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.
