Abstract
We solve a Cauchy problem for a viscoelastic transversely Isotropie medium. Generalizing the method of separation of variables for certain classes of static problems treated in [1], and using this method, we reduce the system of integro-partial differential equations to a system of ordinary differential equations in the time coordinate. Solving the latter system by the method of averaging [2, 3], we obtain explicit formulas characterizing the propagation of waves in a viscoelastic transversely isotropic medium.
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