TY - JOUR
T1 - The Acoustic Scattering of a Layered Elastic Shell Medium
AU - Bao , Gang
AU - Zhang , Lei
JO - Annals of Applied Mathematics
VL - 4
SP - 462
EP - 492
PY - 2023
DA - 2023/11
SN - 39
DO - http://doi.org/10.4208/aam.OA-2023-0019
UR - https://global-sci.org/intro/article_detail/aam/22083.html
KW - Fluid-solid interaction problem, Helmholtz equation, Navier equation, integral operator, index theorem, existence and uniqueness.
AB - <p style="text-align: justify;">This paper investigates the scattering of a three-dimensional elastic
shell scatterer embedded in a layered unbounded structure. The background
structure comprises a two-layer lossy media separated by an unbounded rough
surface. The shell body is filled with an elastic material, the interior of which
is vacuum. Given an incident acoustic point source, our aim is to determine
the acoustic and elastic wave fields in the space. This problem is known as a
fluid-solid interaction problem (FSIP). In this work, the uniqueness of the FSIP
solution is proved by using the integral equation method. Based on the decay
properties of Green’s function, the equivalence of boundary integral equation
systems and the FSIP is established. Since the system of integral equations
containing several integral operators on infinite intervals, we introduce the index theorem of integral operators and analyze the integral operators on infinite
intervals to prove the system of integral equations is Fredholm. We then obtain the uniqueness of the system of integral equations and the corresponding
existence and uniqueness result of the FSIP.</p>