1,721,257 research outputs found
Singular limit of a conserved Penrose-Fife model with special heat flux law and memory effects
No full textA phase-field model of Penrose-Fife type for diffusive phase transitions with conserved order parameter is introduced. A Cauchy-Neumann problem is considered for the related parabolic system which couples a nonlinear Volterra integro-differential equation for the temperature θ with a fourth order relation describing the evolution of the phase variable χ. The latter equation contains a relaxation parameter μ related to the speed of the transition process, which happens to be very small in the applications. Existence and uniqueness for this model as μ > 0 have been recently proved by the first author. Here, the asymptotic behaviour of the model is studied as μ is let tend to zero. By a priori estimates and compactness arguments, the convergence of the solutions is shown. The approximating initial data have to be properly chosen. The problem obtained at the limit turns out to couple the original energy balance equation with an elliptic fourth order inclusion
Existence and uniqueness for the parabolic conserved phase field model with memory
No full textA nonlinear system for the heat diffusion inside a material subject to a phase change is considered. The underlying model is a generalized version of the well-known Caginalp conserved phase-field system, where the Fourier law is replaced by the Coleman-Gurtin heat flux law and a linear growth is allowed for the latent heat density. The resulting problem couples a non-linear parabolic equation derived from the balance of energy with a fourth order parabolic inclusion which rules the evolution of the order parameter . Homogeneous Neumann boundary conditions guarantee that the space-average of is conserved in time. Existence and uniqueness of the solution are proved
Phase change with voids and bubbles
No full textIn this talk we present a result obtained in collaboration with Michel Fremond (Labo-ratoire Central des Ponts et Chaussees, Paris, France) concerning a phase transition modelin which is included the possibility of having voids during the phase change. When looking at frozen ice or cast iron one may see bubbles or voids, they appeared during the water or the melted metal solidification. This aspect is described in the model by the mass balance equation whose effects are included by means of the pressure of the system in the dynamical relations. We present here a well-posedness result for the PDE system associated with the model for a two phase system. Finally, we also discuss the possibility of having voids in the thermo-mechanical evolution of shape memory alloys
Formulazione duale per un modellodi transizione di fase: buona positura e comportamento per tempi lunghi
No full textNonlocal temperature-dependent phase-field models for non-isothermal phase transitions
No full textWe propose a model for non-isothermal phase transitions with non-conserved order parameter driven by a spatially nonlocal free energy with respect to both the temperature and the order parameter. The resulting system of equations is shown to be thermodynamically consistent and to admit a strong solution
A nonlinear degenerating PDE system for phase transitions in thermoviscoelastic materials
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