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加速弛豫增强流导致完全耗散

计算机视觉与模式识别 2024-08-13 v2

作者: Baoyuan Wu , Hongrui Chen , Mingda Zhang , Zihao Zhu , Shaokui Wei , Danni Yuan , Mingli Zhu , Ruotong Wang , Li Liu , Chao Shen

在 arXiv 上查看 ↗ PDF ↗

摘要

我们证明，通过“加速”弛豫增强流，可以构造一个在 $[0,1) \times \mathbb{T}^d$ 上光滑但在 $t=1$ 处高度奇异的流，使得对于任何正扩散系数，与该加速流相关的对流-扩散方程在 $t=1$ 时完全耗散解，将任意初始数据变为常数函数。

关键词

弛豫增强流完全耗散对流-扩散方程奇异流混合增强耗散

引用

@article{arxiv.2401.15002,
  title  = {BackdoorBench: A Comprehensive Benchmark and Analysis of Backdoor Learning},
  author = {Baoyuan Wu and Hongrui Chen and Mingda Zhang and Zihao Zhu and Shaokui Wei and Danni Yuan and Mingli Zhu and Ruotong Wang and Li Liu and Chao Shen},
  journal= {arXiv preprint arXiv:2401.15002},
  year   = {2024}
}

备注

We have uploaded a new version, which can be accessed at arXiv:2407.19845