Reconstruction of small inhomogeneities from boundary measurements:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2004
|
| Schriftenreihe: | Lecture notes in mathematics
1846 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 238 S. graph. Darst. |
| ISBN: | 3540224831 |
Internformat
MARC
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| 100 | 1 | |a Ammari, Habib |d 1969- |e Verfasser |0 (DE-588)129355119 |4 aut | |
| 245 | 1 | 0 | |a Reconstruction of small inhomogeneities from boundary measurements |c Habib Ammari ; Hyeonbae Kang |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2004 | |
| 300 | |a IX, 238 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1846 | |
| 650 | 4 | |a Partielle Differentialgleichung - Inverses Problem - Randwertproblem | |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Inverses Problem |0 (DE-588)4125161-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
| 689 | 0 | 1 | |a Inverses Problem |0 (DE-588)4125161-1 |D s |
| 689 | 0 | 2 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Kang, Hyeonbae |d 1960- |e Verfasser |0 (DE-588)1029525706 |4 aut | |
| 830 | 0 | |a Lecture notes in mathematics |v 1846 |w (DE-604)BV000676446 |9 1846 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012849765&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-012849765 | ||
Datensatz im Suchindex
| _version_ | 1804132833731543040 |
|---|---|
| adam_text | Contents
1 Introduction 1
Part I Detection of Small Conductivity Inclusions
2 Transmission Problem 11
2.1 Some Notations and Preliminaries 11
2.2 Layer Potentials for the Laplacian 14
2.3 Neumann and Dirichlet Functions 30
2.4 Representation Formula 34
2.5 Energy Identities 39
3 Generalized Polarization Tensors 41
3.1 Definition 42
3.2 Uniqueness Result 45
3.3 Symmetry and Positivity of GPT s 47
3.4 Bounds for the Polarization Tensor of Polya Szego 49
3.5 Estimates of the Weighted Volume and the Center of Mass ... 52
3.6 Polarization Tensors of Multiple Inclusions 56
3.6.1 Definition 57
3.6.2 Properties 58
3.6.3 Representation by Equivalent Ellipses 62
4 Derivation of the Full Asymptotic Formula 65
4.1 Energy Estimates 67
4.2 Asymptotic Expansion 71
4.3 Closely Spaced Small Inclusions 76
5 Detection of Inclusions 79
5.1 Constant Current Projection Algorithm 80
5.2 Quadratic Algorithm 85
VIII Contents
5.3 Least Squares Algorithm 88
5.4 Variational Algorithm 89
5.5 Linear Sampling Method 91
5.6 Lipschitz Continuous Dependence and Moments Estimations .. 97
5.6.1 Lipschitz Continuous Dependence 97
5.6.2 Moments Estimations 100
Part II Detection of Small Elastic Inclusions
6 Transmission Problem for Elastostatics 109
6.1 Layer Potentials for the Lame System 109
6.2 Kelvin Matrix Under Unitary Transforms 113
6.3 Transmission Problem 115
6.4 Complex Representation of Displacement Vectors 123
7 Elastic Moment Tensor 129
7.1 Asymptotic Expansion in Free Space 129
7.2 Properties of EMT s 132
7.3 EMT s Under Linear Transforms 140
7.4 EMT s for Ellipses 143
7.5 EMT s for Elliptic Holes and Hard Ellipses 147
8 Derivation of Full Asymptotic Expansions 151
8.1 Full Asymptotic Expansions 151
9 Detection of Inclusions 159
9.1 Detection of EMT s 159
9.2 Representation of the EMT s by Ellipses 163
9.3 Detection of the Location 164
9.4 Numerical Results 167
Part III Detection of Small Electromagnetic Inclusions
10 Well Posedness 179
10.1 Existence and Uniqueness of a Solution 179
11 Representation of Solutions 185
11.1 Preliminary Results 185
11.2 Representation Formulae 188
12 Derivation of Asymptotic Formulae 197
12.1 Asymptotic Expansion 197
Contents IX
13 Reconstruction Algorithms 207
13.1 Asymptotic Expansion 207
13.2 Reconstruction of Multiple Inclusions 209
13.2.1 The Fourier Transform Algorithm 209
13.2.2 The MUSIC Algorithm 213
A Appendices 215
A.I Theorem of Coifman, Mclntosh, and Meyer 215
A.2 Continuity Method 216
A.3 Collectively Compact Operators 217
A.4 Uniqueness for the Inverse Conductivity Problem 217
A.4.1 Uniqueness With Many Measurements 217
A.4.2 Uniqueness of Disks With One Measurement 220
References 223
Index 237
|
| any_adam_object | 1 |
| author | Ammari, Habib 1969- Kang, Hyeonbae 1960- |
| author_GND | (DE-588)129355119 (DE-588)1029525706 |
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| author_role | aut aut |
| author_sort | Ammari, Habib 1969- |
| author_variant | h a ha h k hk |
| building | Verbundindex |
| bvnumber | BV019386886 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| classification_tum | MAT 352f MAT 359f |
| ctrlnum | (OCoLC)249654050 (DE-599)BVBBV019386886 |
| dewey-full | 620.11 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.11 |
| dewey-search | 620.11 |
| dewey-sort | 3620.11 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Allgemeine Naturwissenschaft Mathematik |
| format | Book |
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| id | DE-604.BV019386886 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:59:06Z |
| institution | BVB |
| isbn | 3540224831 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012849765 |
| oclc_num | 249654050 |
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| physical | IX, 238 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Ammari, Habib 1969- Verfasser (DE-588)129355119 aut Reconstruction of small inhomogeneities from boundary measurements Habib Ammari ; Hyeonbae Kang Berlin [u.a.] Springer 2004 IX, 238 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1846 Partielle Differentialgleichung - Inverses Problem - Randwertproblem Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Inverses Problem (DE-588)4125161-1 s Randwertproblem (DE-588)4048395-2 s DE-604 Kang, Hyeonbae 1960- Verfasser (DE-588)1029525706 aut Lecture notes in mathematics 1846 (DE-604)BV000676446 1846 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012849765&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ammari, Habib 1969- Kang, Hyeonbae 1960- Reconstruction of small inhomogeneities from boundary measurements Lecture notes in mathematics Partielle Differentialgleichung - Inverses Problem - Randwertproblem Partielle Differentialgleichung (DE-588)4044779-0 gnd Randwertproblem (DE-588)4048395-2 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4048395-2 (DE-588)4125161-1 |
| title | Reconstruction of small inhomogeneities from boundary measurements |
| title_auth | Reconstruction of small inhomogeneities from boundary measurements |
| title_exact_search | Reconstruction of small inhomogeneities from boundary measurements |
| title_full | Reconstruction of small inhomogeneities from boundary measurements Habib Ammari ; Hyeonbae Kang |
| title_fullStr | Reconstruction of small inhomogeneities from boundary measurements Habib Ammari ; Hyeonbae Kang |
| title_full_unstemmed | Reconstruction of small inhomogeneities from boundary measurements Habib Ammari ; Hyeonbae Kang |
| title_short | Reconstruction of small inhomogeneities from boundary measurements |
| title_sort | reconstruction of small inhomogeneities from boundary measurements |
| topic | Partielle Differentialgleichung - Inverses Problem - Randwertproblem Partielle Differentialgleichung (DE-588)4044779-0 gnd Randwertproblem (DE-588)4048395-2 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Partielle Differentialgleichung - Inverses Problem - Randwertproblem Partielle Differentialgleichung Randwertproblem Inverses Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012849765&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT ammarihabib reconstructionofsmallinhomogeneitiesfromboundarymeasurements AT kanghyeonbae reconstructionofsmallinhomogeneitiesfromboundarymeasurements |