AI 中文总结
本文梳理了经典双尺度收敛与周期展开方法，将其统一到一般双尺度收敛框架，并比较了极弱双尺度收敛与周期展开在放大序列上的差异，兼具综述与新结果。
AI 中文摘要
本文追溯了经典双尺度收敛与周期展开方法（两者均依赖于一个附加尺度来表示周期微观振荡）的根源，将其归结为更广泛的一般双尺度收敛概念。此外，本文还针对在Sobolev空间中受限于微观振荡尺度放大的序列，比较了极弱双尺度收敛与周期展开方法。结果表明，对于放大序列，这些方法并非直接等价。本文既作为文献综述，包含收敛概念的示例与图示，也包含新的结果。
英文摘要
The notions of classical two-scale convergence and the periodic unfolding method, which both rely on an additional scale for the representation of periodic micro-oscillations, are in this paper traced back to the wider concept of general two-scale convergence. Moreover, a comparison is made between very weak two-scale convergence and periodic unfolding with respect to sequences bounded in Sobolev spaces, amplified by the scale of the micro-oscillations. It turns out that, for amplified sequences, these approaches are not equivalent in an immediate sense. The paper both serves as a literature overview, with examples and illustrations of the concepts of convergence, and contains new results.
