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Nonradiating sources of the biharmonic wave equation
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
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