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Title Entropic solutions to a PDE system for phase transitions and damage in thermoviscoelastic materials

Name Riccarda Rossi
Country Italy
Email riccarda.rossi@unibs.it
Co-Author(s) Elisabetta Rocca
Submit Time 2014-02-26 16:43:12
Special Session 2: Nonlinear evolution PDEs and interfaces in applied sciences
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.