论文标题
与空间相关井的均质化和相位分离 - 亚临界情况
Homogenization and phase separation with space dependent wells -- The subcritical case
论文作者
论文摘要
考虑了均质化和相分离之间相互作用的变分模型。重点放在后者发生的制度上，而后者的规模比前者较小，并且当允许双井潜力的井移动并具有不连续性时。确定了零和一阶$γ$限制。后者考虑的拓扑是两个尺度的拓扑，因为它编码了有关渐近局部微观结构的更多信息。特别是，当井不是恒定时，第一阶$γ$限制会描述微观相分离的贡献，在没有宏观相分离的情况下。作为推论，表征了质量约束最小化问题的最小值，并且证明取决于井是否不连续。在证明这些结果的过程中，加强了Modica Mortola功能不均匀的理论。
A variational model for the interaction between homogenization and phase separation is considered. The focus is on the regime where the latter happens at a smaller scale than the former, and when the wells of the double well potential are allowed to move and to have discontinuities. The zeroth and first order $Γ$-limits are identified. The topology considered for the latter is that of two-scale, since it encodes more information on the asymptotic local microstructure. In particular, when the wells are non constant, the first order $Γ$-limit describes the contribution of microscopic phase separation, also in situations where there is no macroscopic phase separation. As a corollary, the minimum of the mass constrained minimization problem is characterized, and it is shown to depend on whether or not the wells are discontinuous. In the process of proving these results, the theory of inhomogeneous Modica Mortola functionals is strengthened.
