| Title:
|
Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes (English) |
| Author:
|
Heinemann, Christian |
| Author:
|
Kraus, Christiane |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
139 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
315-331 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a time-dependent domain which characterizes the nondegenerated elastic material regions. We choose a notion of weak solutions which consists of weak formulations of the Cahn-Hilliard system and the momentum balance equation, a variational inequality for the damage evolution and an energy inequality. For the introduced degenerating system, we prove global-in-time existence of weak solutions. The main results are sketched from our recent paper [WIAS preprint no. 1759 (2012)]. (English) |
| Keyword:
|
Cahn-Hilliard system |
| Keyword:
|
phase separation |
| Keyword:
|
complete damage |
| Keyword:
|
elliptic-parabolic degenerating system |
| Keyword:
|
linear elasticity |
| Keyword:
|
energetic solution |
| Keyword:
|
weak solution |
| Keyword:
|
doubly nonlinear differential inclusion |
| Keyword:
|
existence result |
| Keyword:
|
rate-dependent system |
| MSC:
|
34A12 |
| MSC:
|
35A01 |
| MSC:
|
35D30 |
| MSC:
|
35J50 |
| MSC:
|
35K55 |
| MSC:
|
35K65 |
| MSC:
|
35K85 |
| MSC:
|
35K92 |
| MSC:
|
35M30 |
| MSC:
|
49S05 |
| MSC:
|
74A45 |
| MSC:
|
74G25 |
| MSC:
|
82B26 |
| idZBL:
|
Zbl 06362261 |
| idMR:
|
MR3238842 |
| DOI:
|
10.21136/MB.2014.143857 |
| . |
| Date available:
|
2014-07-14T08:36:15Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143857 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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