Abstract
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 κ. The continuous dependence of the solution with respect to κ is obtained and the problem of finite time stability is also discussed. In the case when κ 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 κ 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.
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Sofonea, M. Some remarks on the behaviour of the solution in dynamic processes for rate-type models. Z. angew. Math. Phys. 41, 656–668 (1990). https://doi.org/10.1007/BF00946099
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DOI: https://doi.org/10.1007/BF00946099