Existence and uniqueness of solutions for a three-dimensional thermoelastic system:
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| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Warszawa
Polska Akad. Nauk, Inst. Matematyczny
2002
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| Schriftenreihe: | Dissertationes mathematicae
406 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 46 S. |
Internformat
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Datensatz im Suchindex
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| adam_text | Titel: Existence and uniqueness of solutions for a three-dimensional thermoelastic system
Autor: Pawlow, Irena
Jahr: 2002
CONTENTS
1. Introduction....................................................................................................................................................5
2. Notation and preliminaries........................................................................................................................8
3. Thermodynamical framework....................................................................................................................10
4. Assumptions and main results..................................................................................................................14
5. Existence proof..............................................................................................................................................16
6. Uniqueness proof............................................................................................................................................29
7. Auxiliary results............................................................................................................................................31
7.1. Parabolicity of systems with elasticity operator........................................................................31
7.2. Additional regularity of solutions..................................................................................................35
7.3. The maximum principle for regular data....................................................................................38
7.4. The stability of solutions.......................................................... 39
7.5. Imbeddings and compactness..........................................................................................................43
References..............................................................................................................................................................44
Abstract
A thermodynamically consistent model of shape memory alloys in three dimensions is studied.
The thermoelastic system, based on the strain tensor, its gradient and the absolute tempera-
ture, is a generalization of the well-known one-dimensional Falk model. The key assumptions
concerning the form of constitutive relations are discussed. The detailed and selfcontained proof
of the global-in-time existence and uniqueness of solutions is presented.
2000 Mathematics Subject Classification: 35Q72, 35K50, 35K60, 74B20.
Key words and phrases: nonlinear thermoelasticity, parabolic regularization, shape memory al-
loys.
Received 19.12.2000; revised 30.10.2001.
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:05:40Z |
| institution | BVB |
| language | English |
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| physical | 46 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | Polska Akad. Nauk, Inst. Matematyczny |
| record_format | marc |
| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Pawlow, Irena Verfasser aut Existence and uniqueness of solutions for a three-dimensional thermoelastic system Irena Pawłow ; Antoni Żochowski Warszawa Polska Akad. Nauk, Inst. Matematyczny 2002 46 S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 406 Shape memory alloys Thermoelasticity Dimension 3 (DE-588)4321722-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Thermoelastizität (DE-588)4185143-2 gnd rswk-swf Thermoelastizität (DE-588)4185143-2 s Dimension 3 (DE-588)4321722-9 s Mathematik (DE-588)4037944-9 s DE-604 Zochowski, Antoni Verfasser aut Dissertationes mathematicae 406 (DE-604)BV000003039 406 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009986245&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pawlow, Irena Zochowski, Antoni Existence and uniqueness of solutions for a three-dimensional thermoelastic system Dissertationes mathematicae Shape memory alloys Thermoelasticity Dimension 3 (DE-588)4321722-9 gnd Mathematik (DE-588)4037944-9 gnd Thermoelastizität (DE-588)4185143-2 gnd |
| subject_GND | (DE-588)4321722-9 (DE-588)4037944-9 (DE-588)4185143-2 |
| title | Existence and uniqueness of solutions for a three-dimensional thermoelastic system |
| title_auth | Existence and uniqueness of solutions for a three-dimensional thermoelastic system |
| title_exact_search | Existence and uniqueness of solutions for a three-dimensional thermoelastic system |
| title_full | Existence and uniqueness of solutions for a three-dimensional thermoelastic system Irena Pawłow ; Antoni Żochowski |
| title_fullStr | Existence and uniqueness of solutions for a three-dimensional thermoelastic system Irena Pawłow ; Antoni Żochowski |
| title_full_unstemmed | Existence and uniqueness of solutions for a three-dimensional thermoelastic system Irena Pawłow ; Antoni Żochowski |
| title_short | Existence and uniqueness of solutions for a three-dimensional thermoelastic system |
| title_sort | existence and uniqueness of solutions for a three dimensional thermoelastic system |
| topic | Shape memory alloys Thermoelasticity Dimension 3 (DE-588)4321722-9 gnd Mathematik (DE-588)4037944-9 gnd Thermoelastizität (DE-588)4185143-2 gnd |
| topic_facet | Shape memory alloys Thermoelasticity Dimension 3 Mathematik Thermoelastizität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009986245&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003039 |
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