二阶奇异扰动相变模型的Γ收敛与随机均匀化
偏微分方程分析
2024-11-07 v4
摘要
我们研究随机、异质、各向异性的二阶相变能的有效行为，这些能量在物理化学系统中的图案形成问题中出现。具体而言，我们研究当 趋于零时，随机异质各向异性函数式的渐近行为，其中二阶扰动不仅与双井势相竞争，还可能与由第一阶项给出的负贡献相竞争。在满足适当增长条件并在某种平稳性假设下，我们证明这些函数式几乎必然收敛于一个表面能，其密度与空间变量无关。 Furthermore, we show that the limit surface density can be described via a suitable cell formula and is deterministic when ergodicity is assumed.
关键词
引用
@article{arxiv.2406.14356,
title = {$\Gamma$-convergence and stochastic homogenization of second order singular perturbation models for phase transitions},
author = {Antonio Flavio Donnarumma},
journal= {arXiv preprint arXiv:2406.14356},
year = {2024}
}
备注
The main changes are the following: in Theorem 3.4 we now also take into account a possible dependence of the limit density on the traces, we have added Remark 4.1 in order to simplify the proof of the fundamental estimate, and the proof of measurability in Proposition 5.4 is now valid in a more general setting