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| We focus on the analysis of a PDE system modelling (non-isothermal) phase transitions
and damage in thermoviscoelastic materials. The model is thermodynamically consistent: in particular, no small perturbation assumption is adopted, which results in the presence of
quadratic terms on the right-hand side of the temperature equation. The whole system has a highly nonlinear character.
We address the existence for a weak notion of solution, referred to as ``entropic'', where the temperature equation is formulated with the aid of an entropy inequality, and of a total energy inequality. This solvability concept reflects the basic principles of
thermomechanics and the thermodynamical consistency of the model, and allows us to obtain \emph{global-in-time} existence theorems without imposing any restriction on the size of the initial data.
We prove our results by passing to the limit in a time-discrete scheme carefully tailored to the nonlinear features of the PDE system and of the a priori estimates performed on it. |
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