Thermoelastic wave scattering by a multi-layered object

In this work the scattering of time -harmonic thermoelastic waves by a multi -layered thermoelastic body is considered. The mathematical formulation of the scattering problem is presented in a unified four-dimensional form. Using the thermoelastic analogue of Betti's identity, the transmission conditions and asymptotic analysis in the dyadic fundamental solution of thermoelasticity, an integral representation of the scattered field as well as formulas of the thermoelastic far -field patterns containing the physical parameters of the scatterer's layers are constructed. Via the Rellich's Lemma for vector fields, the Helmholtz decomposition of thermoelastic waves and the Kupradze's radiation conditions, uniqueness of solution is proved. Setting the solution to be a linear combination of single- and double- layer thermoelastic potentials and using their jump relations, the scattering problem is transformed into a system of integral equations written in a matrix form. Using the regularity properties of the potentials and the Riesz-Fredholm's theory existence of solution is obtained.