Some remarks on the behaviour of the solution in dynamic processes for rate-type models (Q1175772)

The dynamic problem for the semilinear rate-type consitutive equations involving a parameter \(k\) is considered. The continuous dependence of the solution on \(k\) is obtained and the problem of finite time stability is discussed. When \(k\) is the absolute temperature, the dynamic problem is studied in the framework of Cattaneo-type heat law and classical Fourier law. In the case when \(k\) is interpreted to be an internal state variable an existence and uniqueness result is obtained using a fixed point method: the problem of finite time stability is also investigated.