Feynman's Inverse Problem
Abstract
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.
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© 2024, Society for Industrial and Applied Mathematics. This work is licensed under a Creative Commons Attribution 4.0 International License.
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Submitted: 24 October 2023
Accepted: 18 June 2024
Published online: 7 November 2024
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