SIAM Review, Volume 66, Issue 4, Page 694-718, November 2024.
We analyze an inverse problem for water waves posed by Richard Feynman in the BBC documentary Fun to Imagine. We show that the problem can be modeled as an inverse Cauchy problem for gravity-capillary waves, conduct a detailed analysis of the Cauchy problem, and give a uniqueness proof for the inverse problem. Somewhat surprisingly, this results in a positive answer to Feynman's question. In addition, we derive stability estimates for the inverse problem for both continuous and discrete measurements, propose a simple inversion method, and conduct numerical experiments to verify our results.

中文翻译：

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费曼逆问题


SIAM 评论，第 66 卷，第 4 期，第 694-718 页，2024 年 11 月。

我们分析了理查德·费曼 （Richard Feynman） 在 BBC 纪录片《想象的乐趣》中提出的水波逆问题。我们表明，该问题可以建模为引力毛细管波的逆柯西问题，对柯西问题进行详细分析，并为逆问题提供唯一性证明。有点令人惊讶的是，这导致了对 Feynman 问题的肯定回答。此外，我们推导出了连续和离散测量的逆问题的稳定性估计，提出了一种简单的反演方法，并进行了数值实验来验证我们的结果。