| Title:
|
Global solution to a generalized nonisothermal Ginzburg-Landau system (English) |
| Author:
|
Fterich, Nesrine |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
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0862-7940 (print) |
| ISSN:
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1572-9109 (online) |
| Volume:
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55 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
1-46 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The article deals with a nonlinear generalized Ginzburg-Landau (Allen-Cahn) system of PDEs accounting for nonisothermal phase transition phenomena which was recently derived by A. Miranville and G. Schimperna: Nonisothermal phase separation based on a microforce balance, Discrete Contin. Dyn. Syst., Ser. B, {\it 5} (2005), 753--768. The existence of solutions to a related Neumann-Robin problem is established in an $N \le 3$-dimensional space setting. A fixed point procedure guarantees the existence of solutions locally in time. Next, Sobolev embeddings, interpolation inequalities, Moser iterations estimates and results on renormalized solutions for a parabolic equation with $L^1$ data are used to handle a suitable a priori estimate which allows to extend our local solutions to the whole time interval. The uniqueness result is justified by proper contracting estimates. (English) |
| Keyword:
|
nonisothermal Ginzburg-Landau (Allen-Cahn) system |
| Keyword:
|
microforce balance |
| Keyword:
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existence and uniqueness results |
| Keyword:
|
renormalized solutions |
| Keyword:
|
Moser iterations |
| MSC:
|
35K55 |
| MSC:
|
35Q56 |
| MSC:
|
80A22 |
| idZBL:
|
Zbl 1224.35388 |
| idMR:
|
MR2585560 |
| DOI:
|
10.1007/s10492-010-0001-0 |
| . |
| Date available:
|
2010-07-20T13:30:06Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140384 |
| . |
| Reference:
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