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The conserved Penrose–Fife system with temperature-dependent memory

✍ Scribed by Elisabetta Rocca

Book ID
104151167
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
283 KB
Volume
287
Category
Article
ISSN
0022-247X

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✦ Synopsis

A nonlinear parabolic system of Penrose-Fife type with a singular evolution term, arising from modelling dynamic phenomena of the nonisothermal diffusive phase separation, is studied. Here, we consider the evolution of a material in which the heat flux is a superposition of two different contributions: one part is proportional to the spacial gradient of the inverse of the absolute temperature ϑ, while the other agrees with the Gurtin-Pipkin law, introduced in the theory of materials with thermal memory. The phase transition here is described through the evolution of the conserved order parameter χ, which may represent the density or concentration of some substance. It is shown that an initial-boundary value problem for the resulting state equations has a unique solution.

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## Abstract We deal with the Dirichlet problem for a class of Penrose–Fife phase field models for phase transitions. An existence result is obtained by approximating the non‐homogeneous Dirichlet condition with classical third type conditions on the heat flux at the boundary of the domain where the