| Title:
|
Well-posedness and regularity for a parabolic-hyperbolic Penrose-Fife phase field system (English) |
| Author:
|
Rocca, Elisabetta |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
50 |
| Issue:
|
5 |
| Year:
|
2005 |
| Pages:
|
415-450 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This work is concerned with the study of an initial boundary value problem for a non-conserved phase field system arising from the Penrose-Fife approach to the kinetics of phase transitions. The system couples a nonlinear parabolic equation for the absolute temperature with a nonlinear hyperbolic equation for the phase variable $\chi $, which is characterized by the presence of an inertial term multiplied by a small positive coefficient $\mu $. This feature is the main consequence of supposing that the response of $\chi $ to the generalized force (which is the functional derivative of a free energy potential and arises as a consequence of the tendency of the free energy to decay towards a minimum) is subject to delay. We first obtain well-posedness for the resulting initial-boundary value problem in which the heat flux law contains a special function of the absolute temperature $\vartheta $, i.e. $\alpha (\vartheta )\sim \vartheta -1/\vartheta $. Then we prove convergence of any family of weak solutions of the parabolic-hyperbolic model to a weak solution of the standard Penrose-Fife model as $\mu \searrow 0$. However, the main novelty of this paper consists in proving some regularity results on solutions of the parabolic-hyperbolic system (including also estimates of Moser type) that could be useful for the study of the longterm dynamics. (English) |
| Keyword:
|
Penrose-Fife model |
| Keyword:
|
hyperbolic equation |
| Keyword:
|
continuous dependence |
| Keyword:
|
regularity |
| MSC:
|
35B45 |
| MSC:
|
35B65 |
| MSC:
|
35G25 |
| MSC:
|
80A22 |
| idZBL:
|
Zbl 1099.35021 |
| idMR:
|
MR2160071 |
| DOI:
|
10.1007/s10492-005-0031-1 |
| . |
| Date available:
|
2009-09-22T18:23:25Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134616 |
| . |
| Reference:
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