George Chkadua
abstract:
In the paper, is consider a three-dimensional model of fluid-solid acoustic
interaction when an electro-magneto-elastic body occupying a bounded region
$\Omega^{+}$ is embedded in an unbounded fluid domain $\Omega^{-}=\mathbb{R}^3
\setminus \overline{\Omega^+}$. In this case in the domain $\Omega^{+}$ is a
five-dimensional electro-magneto-elastic field (the displacement vector with
three components, electric potential and magnetic potential), while in the
unbounded domain $\Omega^{-}$ is a scalar acoustic pressure field. The physical
kinematic and dynamic relations mathematically are described by appropriate
boundary and transmission conditions. In the paper, less restrictions are
considered on matrix differential operator of electro-magneto-elasticity and
asymptotic classes are introduced. In particular, corresponding characteristic
polynomial of the matrix differential operator can have multiple real zeros.
With the help of the potential method and theory of pseudodifferential
equations, for above mentioned fluid-solid acoustic interaction mathematical
problems the uniqueness and existence theorems are proved in
Sobolev-Slobodetskii spaces.
Mathematics Subject Classification: 35J47, 74F15, 31B10, 34L2540
Key words and phrases: Boundary-transmission problems, fluid-solid interaction, potential method, pseudodifferential equations, Helmholtz equation, steady state oscillations, Jones modes, Jones eigenfrequencies