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Well-posedness and regularity for a parabolic-hyperbolic Penrose-Fife phase field system

Elisabetta Rocca — 2005

Applications of Mathematics

This work is concerned with the study of an initial boundary value problem for a non-conserved phase field system arising from the Penrose-Fife approach to the kinetics of phase transitions. The system couples a nonlinear parabolic equation for the absolute temperature with a nonlinear hyperbolic equation for the phase variable χ , which is characterized by the presence of an inertial term multiplied by a small positive coefficient μ . This feature is the main consequence of supposing that the response...

Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials

Elisabetta RoccaRiccarda Rossi — 2008

Applications of Mathematics

This paper is devoted to the analysis of a one-dimensional model for phase transition phenomena in thermoviscoelastic materials. The corresponding parabolic-hyperbolic PDE system features a internal energy balance equation, governing the evolution of the absolute temperature ϑ , an evolution equation for the phase change parameter χ , including constraints on the phase variable, and a hyperbolic stress-strain relation for the displacement variable 𝐮 . The main novelty of the model is that the equations...

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