The problem of determining the one-dimensional kernel for the system of viscoelasticity in the anisotropic medium

We pose the direct and inverse problem of finding the acoustic wave velocity and pressure, diagonal memory matrix for a reduced canonical system of integro-differential acoustic equations. The problems are replaced by a closed system of Volterra-type integral equations of the second kind with respect to the Fourier transform in the variables x1 and x2 of the solution of the unknowns of the direct problem and the inverse problem. To this system, we then apply a reduction method, a mapping in the space of continuous functions with a weighted norm. Thus, we prove global existence and uniqueness theorems to solve the given problems.

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