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

Elisabetta Rocca

Displaying similar documents to “Well-posedness and regularity for a parabolic-hyperbolic Penrose-Fife phase field system”

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

Elisabetta Rocca, Riccarda Rossi (2008)

Applications of Mathematics

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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...

On a conserved Penrose-Fife type system

Gianni Gilardi, Andrea Marson (2005)

Applications of Mathematics

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We deal with a class of Penrose-Fife type phase field models for phase transitions, where the phase dynamics is ruled by a Cahn-Hilliard type equation. Suitable assumptions on the behaviour of the heat flux as the absolute temperature tends to zero and to $+ \infty$ are considered. An existence result is obtained by a double approximation procedure and compactness methods. Moreover, uniqueness and regularity results are proved as well.

Global existence for the conserved phase field model with memory and quadratic nonlinearity.

Colli, P., Gilardi, G., Grasselli, M., Schimperna, G. (2001)

Portugaliae Mathematica. Nova Série

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Well-posedness results for a model of damage in thermoviscoelastic materials

Elena Bonetti, Giovanna Bonfanti (2008)

Annales de l'I.H.P. Analyse non linéaire

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Quasilinear hyperbolic equations with hysteresis

Augusto Visintin (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Hysteresis operators are illustrated, and a weak formulation is studied for an initial- and boundary-value problem associated to the equation $(\partial^{2} / \partial t^{2}) [u + F (u)] + A u = f$ ; here $F$ is a (possibly discontinuous) hysteresis operator, $A$ is a second order elliptic operator, $f$ is a known function. Problems of this sort arise in plasticity, ferromagnetism, ferroelectricity, and so on. In particular an existence result is outlined.