George Chkadua

Solvability of the Mixed Type Interaction Problem of Acoustic Waves and Electro-Magneto-Elastic Structures

abstract:
In the present paper, we 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, we have a five-dimensional electro-magneto-elastic field (the displacement vector with three components, electric potential and magnetic potential) in the domain $\Omega^{+}$, while we have a scalar acoustic pressure field in the unbounded domain $\Omega^{-}$. The physical kinematic and dynamic relations are described mathematically by appropriate boundary and transmission conditions. We consider less restrictions on matrix differential operator of electro-magneto-elasticity by introducing asymptotic classes, in particular, we allow the corresponding characteristic polynomial of the matrix operator to have multiple real zeros. Using the potential method and the theory of pseudodifferential equations based on the Wiener--Hopf factorization method, 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