Nonradiating sources of the biharmonic wave equation
Year: 2024
Type: article
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.
Source: Inverse Problems and Imaging
DOI: 10.3934/ipi.2024056
Authors: Peijun Li, Jue Wang
Institution: Hangzhou Normal University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4405889536