A Uniqueness Theorem for Free Waves on $\mathbb{R}^{n+1}$
Phillip Whitman, Pin Yu
TL;DR
This paper establishes a converse to the classical Huygens principle for free wave equations on Euclidean space using Carleman estimates and Holmgren's theorems, with discussions on potential generalizations.
Contribution
It introduces a new converse theorem for the Huygens principle for free waves, expanding understanding of wave propagation and uniqueness.
Findings
Proves a converse theorem for free wave equations.
Uses Carleman estimates and Holmgren's theorems.
Discusses potential extensions to other space-times.
Abstract
In this short note, based on Carleman estimates and Holmgren's type theorems, we provide a converse theorem of the classical Huygens principle for free wave equations. Possible generalizations to other underlying space-times or other wave type equations are also discussed.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Mathematical Analysis and Transform Methods