AI 中文总结
本文研究带第三类传输条件的Cahn--Hilliard系统，分析渗透率参数趋于零（完全不可渗透边界）与无穷（完全可渗透边界）时的渐近行为，建立解的收敛性并刻画极限方程。
AI 中文摘要
本文研究的系统中，体域内施加Cahn--Hilliard系统，边界上指定Allen--Cahn型方程，二者通过以渗透率参数为特征的第三类传输条件连接。该设定与传输问题理论密切相关，第三类传输条件可视为薄边界描述的残余，渗透率参数控制体域与边界间的耦合程度。主要目标是针对渗透率参数开展严格渐近分析，研究两种极限情形：参数趋于零对应完全不可渗透边界，参数趋于无穷对应体相与边界相完全耦合的完全可渗透边界。对每种极限 regime，本文建立解到对应极限问题的收敛性，并刻画所得方程。
英文摘要
In this paper, we study a system in which the Cahn--Hilliard system is imposed in the bulk domain and an Allen--Cahn type equation is prescribed on the boundary, connected through a third type transmission condition characterized by a permeability parameter. This setting is closely related to the theory of transmission problems, and the third type transmission condition can be viewed as a remnant of a thin-boundary description, with the permeability parameter controlling the degree of coupling between the bulk and the boundary. The main objective is to perform a rigorous asymptotic analysis with respect to the permeability parameter. We investigate two limits: the parameter tending to zero, corresponding to a completely impermeable boundary, and the parameter tending to infinity, corresponding to a perfectly permeable boundary where the bulk and boundary phases are fully coupled. For each limiting regime, we establish the convergence of solutions to the respective limit problems and characterize the resulting equations.
Comments29 pages
