Global Well-Posedness for a Phase Transition Model with Irreversible Evolution and Acceleration Forces

2017 ◽  
pp. 97-117
Author(s):  
Giovanna Bonfanti ◽  
Fabio Luterotti
Keyword(s):  
Phase Transition ◽  
Transition Model ◽  
Well Posedness ◽  
Irreversible Evolution

WELL-POSEDNESS OF A PHASE TRANSITION MODEL WITH THE POSSIBILITY OF VOIDS

2006 ◽  
Vol 16 (04) ◽  
pp. 559-586 ◽  
Author(s):  
MICHEL FRÉMOND ◽  
ELISABETTA ROCCA
Keyword(s):  
Phase Transition ◽  
Balance Equation ◽  
Strain Tensor ◽  
Absolute Temperature ◽  
Phase System ◽  
Transition Model ◽  
Well Posedness ◽  
State Variables ◽  
Two Phase ◽  
Two Phases

The paper deals with a phase transition model applied to a two-phase system. There is a wide literature on the study of phase transition processes in case that no voids nor overlapping can occur between the two phases. The main novelty of our approach is the possibility of having voids during the phase change. 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. The state variables are the absolute temperature (whose evolution is ruled by the entropy balance equation), the strain tensor (satisfying a quasi-static macroscopic equation of motion), and the volume fractions of the two phases (whose evolutions are described by a vectorial equation coming from the principle of virtual power and related to the microscopic motions). Well-posedness of the initial-boundary value problem associated to the PDEs system resulting from this model is proved.

WELL POSEDNESS FOR A PHASE TRANSITION MODEL IN SUPERCONDUCTIVITY WITH VELOCITY AND MAGNETIC CRITICAL FIELDS

2009 ◽  
Vol 19 (01) ◽  
pp. 1-30 ◽  
Author(s):  
V. BERTI ◽  
M. FABRIZIO
Keyword(s):  
Phase Transition ◽  
Thermal Effects ◽  
Transition Model ◽  
Well Posedness ◽  
Threshold Values ◽  
Critical Fields ◽  
Ginzburg Landau ◽  
Fixed Parameter ◽  
Superconducting Current ◽  
The Magnetic Field

In this paper we present a Ginzburg–Landau model to describe the phenomenon of superconductivity as a second-order phase transition. The model proposed, which also includes thermal effects, allows to explain the existence of threshold values, both of the magnetic field and of the superconducting current, beyond which superconductivity vanishes. This is achieved by introducing a constitutive equation for the magnetic induction where the magnetic permeability depends on the complex order parameter. The model is proved to be consistent with thermodynamical principles. The resulting differential system is studied under the assumption that the temperature is a fixed parameter and its well-posedness is proved.

CONVERGENCE RESULTS FOR A PHASE TRANSITION MODEL WITH VANISHING MICROSCOPIC ACCELERATION

2004 ◽  
Vol 14 (03) ◽  
pp. 375-392 ◽  
Author(s):  
GIOVANNA BONFANTI ◽  
FABIO LUTEROTTI
Keyword(s):  
Phase Transition ◽  
Asymptotic Behavior ◽  
Transition Model ◽  
Well Posedness ◽  
Macroscopic Level ◽  
Neumann Problems ◽  
Convergence Results ◽  
Recent Phase

A recent phase transition model, proposed by Frémond, is based on the consideration that the microscopic movements are responsible for the phase transition at the macroscopic level. A last version of the model, accounting also for the microscopic accelerations has been investigated in Ref. 4, where well-posedness results are established for related Cauchy–Neumann problems. The aim of this paper is the study of the asymptotic behavior of the solution to one of the above problems, as the power of the microscopic acceleration forces goes to zero.

Analysis of a thermomechanical phase transition model

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 1150805-1150806 ◽  
Author(s):  
Krzysztof CheÅ‚miński ◽  
Dietmar Hömberg ◽  
Daniela Kern
Keyword(s):  
Phase Transition ◽  
Transition Model

scholarly journals A Phase Transition Model of Cooperative Phenomena in Membranes.

1986 ◽  
Vol 40b ◽  
pp. 1-5 ◽  
Author(s):  
Kåre Larsson ◽  
Sten Andersson ◽  
Torbjörn Drakenberg ◽  
Curt R. Enzell ◽  
Synnøve Liaaen-Jensen ◽  
...  
Keyword(s):  
Phase Transition ◽  
Transition Model ◽  
Cooperative Phenomena

scholarly journals Stationary patterns for an adsorbate-induced phase transition model I: Existence

2010 ◽  
Vol 14 (3) ◽  
pp. 1105-1117 ◽  
Author(s):  
Kousuke Kuto ◽  
◽  
Tohru Tsujikawa ◽  
Keyword(s):  
Phase Transition ◽  
Transition Model

scholarly journals Long time behaviour of a singular phase transition model

2006 ◽  
Vol 15 (4) ◽  
pp. 1119-1135 ◽  
Author(s):  
Pavel Krejčí ◽  
◽  
Jürgen Sprekels
Keyword(s):  
Phase Transition ◽  
Transition Model ◽  
Time Behaviour ◽  
Long Time Behaviour ◽  
Long Time
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