论文标题
De Gennes-Cahn-Hilliard Energy的伽马收敛
Gamma Convergence for the de Gennes-Cahn-Hilliard energy
论文作者
论文摘要
退化的DE GENNES-CAHN-HILLIARD（DGCH）方程是一个相分离的模型，当过渡层的厚度接近零时，与其他限制相比，在极限中的表面扩散可能更接近。作为了解限制行为的第一步，在本文中，我们研究了DGCH能量的$γ$ - 限制。我们发现它的$γ$ - 极限是界面区域的常数倍数，在该界面区域，该常数由DE GENNES系数以及双井电位确定。相比之下，过渡层的轮廓仅由双井电位确定。
The degenerate de Gennes-Cahn-Hilliard (dGCH) equation is a model for phase separation which may more closely approximate surface diffusion than others in the limit when the thickness of the transition layer approaches zero. As a first step to understand the limiting behavior, in this paper we study the $Γ$--limit of the dGCH energy. We find that its $Γ$--limit is a constant multiple of the interface area, where the constant is determined by the de Gennes coefficient together with the double well potential. In contrast, the transition layer profile is solely determined by the double well potential.
