发表机构
Politecnico di Bari; University of Western Australia（巴里理工大学; 西澳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究一维周期线性近场动力学波模型，构造显式解证明初始跳跃间断随时间消散，并通过时间可逆性实现连续初值在指定时刻产生跳跃，且量化奇点形成，最终构造稠密时间集上的间断演化。
AI 中文摘要
我们分析了一维周期线性近场动力学波模型的解，重点关注自然能量空间允许空间间断的情形。利用近场动力学色散关系的高频渐近性，我们构造了一个显式解，其初始位移具有单个跳跃间断，但在每个正时刻变得连续。通过时间可逆性，这产生了一个连续的初始位移，其演化在任意规定时刻发展出跳跃，并在其他所有时刻连续。我们进一步通过Hölder空间的Littlewood-Paley刻画获得的尖锐Hölder范数爆破估计来量化该奇点的形成。最后，通过叠加适当加权的解，我们构造了一个在时间稠密集合上表现出跳跃间断的演化。
英文摘要
We analyze solutions to a one-dimensional periodic linear model for peridynamic waves, focusing on the setting where the natural energy space allows for spatial discontinuities. Exploiting the high-frequency asymptotics of the peridynamic dispersion relation, we construct an explicit solution whose initial displacement has a single jump discontinuity but becomes continuous at every positive time. By time reversibility, this yields a continuous initial displacement whose evolution develops a jump at any prescribed time and is continuous at every other time. We further quantify the formation of this singularity through a sharp Hölder-norm blow-up estimate obtained via a Littlewood-Paley characterization of Hölder spaces. Finally, by superposing suitably weighted solutions, we construct an evolution exhibiting jump discontinuities on a dense set of times.
