Analysis of a nonlinear degenerating PDE system for phase transitions in thermoviscoelastic materials
Articolo
Data di Pubblicazione:
2008
Citazione:
Analysis of a nonlinear degenerating PDE system for phase transitions in thermoviscoelastic materials / E. Rocca, R. Rossi. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 245:11(2008), pp. 3327-3375.
Abstract:
We address the analysis of a nonlinear and degenerating PDE system, proposed by M. Frémond for modelling
phase transitions in viscoelastic materials subject to thermal effects. The system features an internal
energy balance equation, governing the evolution of the absolute temperature ϑ, an evolution equation for
the phase change parameter χ, and a stress–strain relation for the displacement variable u. The main novelty
of the model is that the equations for χ and u are coupled in such a way as to take into account the fact that
the properties of the viscous and of the elastic parts influence the phase transition phenomenon in different
ways. However, this brings about an elliptic degeneracy in the equation for u which needs to be carefully
handled.
In this paper, we first prove a local (in time) well-posedness result for (a suitable initial–boundary value
problem for) the above mentioned PDE system, in the (spatially) three-dimensional setting. Secondly, we
restrict to the one-dimensional case, in which, for the same initial–boundary value problem, we indeed
obtain a global well-posedness theorem.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Local and global existence; Nonlinear and degenerating PDE system; Phase transitions; Thermoviscoelastic materials; Uniqueness
Elenco autori:
E. Rocca, R. Rossi
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