The problem of finding the kernels in the system of integro-differential acoustics equations

For reduced to the canonical system of integro-differential equations of acoustics, a direct problem is posed, which consists in determining the velocity of the perturbed medium and the pressure and the inverse problem of finding the diagonal memory matrix. The problems are reduced to a closed system of integral equations of the second kind of the Volterra type with respect to the solution of the direct problem and unknowns of the inverse problem. The method of contraction mappings in the space of continuous functions with an exponential weighted norm is applied to this system. Existence and uniqueness theorems for solutions to problems in the global sense are proved.