带约束的Landau-Brazovskii模型的非平凡周期极小解
Nontrivial Periodic Minimizer for Landau-Brazovskii Model with Constraint
摘要：
嵌段共聚物是一种合成高分子材料，在工业上有着广泛的应用。它是由多个序列的单体交替串联不同的单体嵌段。不同聚合物的组合赋予了高分子材料丰富的性能，这些性能是其重要应用的关键。在本文中，我们用Landau-Brazovskii模型来模拟共聚物，该模型具有反映物理结构的附加约束，其形式为二阶变分问题。泛函的临界点被解释为聚合物的状态。通过简化到方便的情况，我们找到了一个非平凡的周期极小解。此外，在我们的具体情况下，证明尽可能简单和独立。
英文摘要：
Block copolymer, a synthesized polymer material, has found many applications in industry. It is consisting of multiple sequences of monomer alternating in series with different monomer blocks. The combination of different polymers endows the polymer material with rich properties, which are the key to their important applications. In this paper, we model the copolymers with Landau-Brazovskii model with additional constraints reflecting physical structures, which is in the form of a second order variational problem. Critical points of the functional are interpreted as states of polymers. By reducing to handy situations, we find a nontrivial periodic minimal solution. Moreover, the proof is kept as simple and self-contained as possible in our specific case.
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