Periodic propagation of singularities for heat equations with time delay
Wang G, Yu H, Zhang Y (2026)
Publication Type: Journal article
Publication year: 2026
Journal
Book Volume: 469
Article Number: 114347
DOI: 10.1016/j.jde.2026.114347
Abstract
This paper presents two remarkable phenomena associated with the heat equation with a time delay: namely, the propagation of singularities and periodicity. These are manifested through a distinctive mode of propagation of singularities in the solutions. Precisely, the singularities of the solutions propagate periodically in a bidirectional fashion along the time axis. Furthermore, this propagation occurs in a stepwise manner. More specifically, when propagating in the positive time direction, the order of the joint derivatives of the solution increases by 2 for each period; conversely, when propagating in the reverse time direction, the order of the joint derivatives decreases by 2 per period. Additionally, we elucidate the way in which the initial data and historical values impact such propagation of singularities. The phenomena we have discerned corroborate the pronounced differences between heat equations with and without time delay, especially from the point of view of propagation of singularities.
Involved external institutions
China (CN)How to cite
APA:
Wang, G., Yu, H., & Zhang, Y. (2026). Periodic propagation of singularities for heat equations with time delay. Journal of Differential Equations, 469. https://doi.org/10.1016/j.jde.2026.114347
MLA:
Wang, Gengsheng, Huaiqiang Yu, and Yubiao Zhang. "Periodic propagation of singularities for heat equations with time delay." Journal of Differential Equations 469 (2026).
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