Stability of viscoelastic solid systems with monotone relaxation

The paper deals with the stability of viscoelastic continuous systems. By starting from the fundamental assumption of monotonicity for the first and second temporal derivative of the operator describing system relaxation, it is possible to build up a Liapunov functional which permits recognizing a class of stable motions. This makes it possible to perform a stability analysis by means of a direct method and bypass the difficulty encountered in the past in determining the progress in time of evolution systems of this kind. The stability problems involving viscoelastic solids are presented in a unitary form which evidences the common structure and the peculiarities of the operator. An application of the method is also reported