Mixed-type dynamical interaction problem of acoustic waves and thermo-electro-magneto-elastic solids

Abstract

In the paper, we consider a three-dimensional dynamical model of fluid-solid interaction in which a generalized thermo-electro-magneto-elastic body occupying a bounded region

is embedded in an inviscid fluid occupying an unbounded domain

Ω - = ℝ 3 ∖ Ω + ¯ {\Omega^{-}=\mathbb{R}^{3}\setminus\overline{\Omega^{+}}}

. In this case, we have a six-dimensional Green–Lindsay’s model of the generalized dynamical thermo-electro-magneto-elastic field (consisting of the displacement vector with three components, electric potential, magnetic potential, and temperature distribution function) in the domain

Ω + {\Omega^{+}}

, while we have a scalar acoustic pressure field in the unbounded domain

Ω - {\Omega^{-}}

. The physical kinematic and dynamic relations are described mathematically by appropriate boundary and transmission conditions. Using the Laplace transform, the dynamical interaction mixed-type problem is reduced to the corresponding interaction problem for elliptic pseudo-oscillation equations containing a complex parameter τ. We derive the appropriate norm estimates with respect to the complex parameter τ and construct the solution of the original dynamical mixed-type problem by the inverse Laplace transform. As a result, we prove the uniqueness and existence of a solution for the dynamical interaction mixed-type problem.