Nonradiating sources of the biharmonic wave equation
Analysis of PDEs
2023-09-06 v1 Mathematical Physics
math.MP
Abstract
This paper offers an extensive exploration of nonradiating sources for the two- and three-dimensional biharmonic wave equations. Various equivalent characterizations are derived to reveal the nature of a nonradiating source. Additionally, we establish the connection between nonradiating sources in the biharmonic wave equation and those in the Helmholtz equation as well as the modified Helmholtz equation. Several illustrative examples are explicitly constructed to showcase the existence of nonradiating sources. One significant implication of the existence of nonradiating sources is that it undermines the uniqueness of the inverse source problem when utilizing boundary data at a fixed frequency.
Keywords
Cite
@article{arxiv.2309.01058,
title = {Nonradiating sources of the biharmonic wave equation},
author = {Peijun Li and Jue Wang},
journal= {arXiv preprint arXiv:2309.01058},
year = {2023}
}