The solution of a one-dimensional Stefan problem:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
Centrum voor Wiskunde en Informatica
1993
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| Series: | Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract
90 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 134 S. graph. Darst. |
| ISBN: | 9061964199 |
Staff View
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| 245 | 1 | 0 | |a The solution of a one-dimensional Stefan problem |c C.Vuik |
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| 650 | 7 | |a Partiële differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Probleem van Stefan |2 gtt | |
| 650 | 7 | |a Problèmes aux limites |2 ram | |
| 650 | 7 | |a Équations intégrales |2 ram | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Heat equation | |
| 650 | 4 | |a Integral equations | |
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Record in the Search Index
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| adam_text | Contents
0 Introduction and summary 1
0.1 The origin of the Stefan problem 1
0.2 Historical survey 1
0.3 Summary of this monograph 4
0.3.1 Introduction 4
0.3.2 Chapter 1 6
0.3.3 Chapter 2 9
0.3.4 Chapter 3 10
References 13
1 The solution of a one dimensional Stefan problem I 14
1.1 Introduction 14
1.2 Preliminaries 16
1.2.1 Definitions 16
1.2.2 Function spaces 16
1.2.3 Existence theorems and maximum principle 17
1.2.4 Approximation results 20
1.3 Statement of the problem 23
1.4 Properties of the reduced problem 25
1.4.1 Existence theorem I 25
1.4.2 Estimation of 2fj£ 26
1.4.3 The relation fs(t) = / 2£ (S(t),t) It 28
o
1.4.4 Existence theorem II 30
1.4.5 fs depends continuously on S 33
1.4.6 Properties of the function fg 34
1.4.7 Existence theorem III 35
1.5 The solution of the Stefan problem 37
1.5.1 Definition of the operator T 37
1.5.2 Existence and uniqueness of the solution for the Stefan problem 38
1.5.3 Further uniqueness results 40
1.6 Applications of our Main theorems 42
1.6.1 The classical Stefan problem 42
1.6.2 Other examples 44
1.6.3 Numerical experiments 48
References 53
Figures 55
2 The solution of a one dimensional Stefan problem II 60
2.1 Introduction 60
2.2 Statement of the problem 62
2.2.1 Definitions 62
2.2.2 Function spaces 62
2.2.3 Statement of the problem 63
2.3 Preliminaries 65
2.4 The solution of the Stefan problem 67
2.4.1 An estimation of the quantity ||/s, — fs2 i,oo 67
2.4.2 Definition of the operator T 73
2.4.3 Existence and uniqueness of the solution of the Stefan problem 74
2.5 Application of the main theorem 78
2.5.1 Examples 78
2.5.2 Invariance properties of the reduced and Stefan problem 81
2.5.3 Numerical experiments 85
2.5.4 Example where Co is such that lim C0(x) 0 86
References 91
Figures 92
3 The solution of a one dimensional Stefan problem III 95
3.1 Introduction 95
3.2 Statement of the problem 97
3.2.1 Definitions 97
3.2.2 Function spaces 97
3.2.3 Conditions 98
3.2.4 Statement of a Stefan problem 102
3.3 Preliminaries 102
3.3.1 Known results 103
3.3.2 Approximation results 104
3.4 Properties of the reduced problem 106
3.4.1 Estimation of —f 106
3.4.2 Existence results for Cs 108
3.4.3 Properties of the function fs 109
3.5 The solution of the Stefan problem 113
3.5.1 Definition of the operator T 113
3.5.2 Fixed point theorems for the operator T 114
3.5.3 Existence and uniqueness of the. solution of the Stefan problem 116
3.6 Examples and numerical experiments 119
3.6.1 Examples 120
3.6.2 Numerical experiments 125
References 128
Figures 130
Index 133
|
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV009823240 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:41:31Z |
| institution | BVB |
| isbn | 9061964199 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006503040 |
| oclc_num | 29243752 |
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| owner | DE-91G DE-BY-TUM DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-188 |
| physical | 134 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Centrum voor Wiskunde en Informatica |
| record_format | marc |
| series | Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract |
| spelling | Vuik, Cornelis Verfasser aut The solution of a one-dimensional Stefan problem C.Vuik Amsterdam Centrum voor Wiskunde en Informatica 1993 134 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract 90 Partiële differentiaalvergelijkingen gtt Probleem van Stefan gtt Problèmes aux limites ram Équations intégrales ram Boundary value problems Heat equation Integral equations (DE-588)4113937-9 Hochschulschrift gnd-content Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract 90 (DE-604)BV001902011 90 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006503040&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vuik, Cornelis The solution of a one-dimensional Stefan problem Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract Partiële differentiaalvergelijkingen gtt Probleem van Stefan gtt Problèmes aux limites ram Équations intégrales ram Boundary value problems Heat equation Integral equations |
| subject_GND | (DE-588)4113937-9 |
| title | The solution of a one-dimensional Stefan problem |
| title_auth | The solution of a one-dimensional Stefan problem |
| title_exact_search | The solution of a one-dimensional Stefan problem |
| title_full | The solution of a one-dimensional Stefan problem C.Vuik |
| title_fullStr | The solution of a one-dimensional Stefan problem C.Vuik |
| title_full_unstemmed | The solution of a one-dimensional Stefan problem C.Vuik |
| title_short | The solution of a one-dimensional Stefan problem |
| title_sort | the solution of a one dimensional stefan problem |
| topic | Partiële differentiaalvergelijkingen gtt Probleem van Stefan gtt Problèmes aux limites ram Équations intégrales ram Boundary value problems Heat equation Integral equations |
| topic_facet | Partiële differentiaalvergelijkingen Probleem van Stefan Problèmes aux limites Équations intégrales Boundary value problems Heat equation Integral equations Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006503040&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001902011 |
| work_keys_str_mv | AT vuikcornelis thesolutionofaonedimensionalstefanproblem |