Some remarks on the behaviour of the solution in dynamic processes for rate-type models

This work examines a dynamic problem in the study of semilinear rate-type models for which the plastic rate of deformation depends also on a parameter . The continuous dependence of the solution with respect to is obtained and the problem of finite time stability is also discussed. In the case when is interpreted as the absolute temperature, the dynamic problem is studied in the context of a Cattaneo-type heat law and also using the classical Fourier law. In the case when is interpreted as an internal state variable an existence and uniqueness result is obtained using a fixed point method and the finite time stability is also investigated.