Inverse source problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1990]
|
| Series: | Mathematical surveys and monographs
Number 34 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiv, 193 Seiten |
| ISBN: | 0821815326 9780821815328 |
Staff View
MARC
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| 245 | 1 | 0 | |a Inverse source problems |c Victor Isakov |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1990] | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
Foreword xi
Chapter 1. Preliminaries 1
1.1. Sets and functions. Differential operators 1
1.2. Uniqueness of the continuation 4
1.3. Elliptic boundary value problems for second order equations 10
1.4. Fundamental solutions 14
1.5. Measures and their potentials 15
1.6. Properties of volume and simple layer potentials 18
1.7. Stability of the Dirichlet problem 22
1.8. The sweeping out method of Poincare 27
Chapter 2. Results Overlook 33
2.1. Problem formulation 33
2.2. Uniqueness results 36
2.3. Stability and the numerical solution 38
2.4. Existence problem 43
2.5. Use of one complex variable 46
2.6. Nonstationary problems 48
Chapter 3. Uniqueness Theorems 55
3.1. Unknown domain 55
3.2. Unknown domain and density 62
3.3. Unknown density 64
3.4. Examples of nonuniqueness 68
3.5. Methods of the Fourier transform 76
3.6. Stability estimates 80
3.7. Commentary 84
Chapter 4. Singular Points of the Exterior Potential 89
4.1. Regularity and analyticity of domains and their potentials 89
4.2. Singularities of the corner potentials 94
4.3. Singularities and the Fourier transform 97
vii
viii CONTENTS
4.4. Computation of some potentials 99
4.5. Commentary 103
Chapter 5. Existence Theory 105
5.1. Local existence theorems 105
5.2. On global existence of a solution 110
5.3. Proofs of local theorems 112
5.4. An analogy of Korn Lichtenstein Giraud s inequality 119
5.5. Proof of Theorem 5.1.7 in the plane case 129
5.6. Existence theorem for the density problem 133
5.7. Commentary 135
Chapter 6. Parabolic Problems 137
6.1. Preliminaries 137
6.2. The final overdetermination 142
6.3. A lateral overdetermination: df/dxn = 0 149
6.4. A lateral overdetermination: df/dt = 0 152
6.5. A domain problem 154
6.6. Commentary 159
Chapter 7. Hyperbolic Problems 161
7.1. Preliminaries 161
7.2. On the final overdetermination 164
7.3. The lateral overdetermination: n = 1 166
7.4. The lateral overdetermination: the density problem for 2 n 170
7.5. Recovering a domain 173
7.6. Commentary 180
Bibliography 181
Index 193
|
| any_adam_object | 1 |
| author | Isakov, Victor 1947- |
| author_GND | (DE-588)118129570 |
| author_facet | Isakov, Victor 1947- |
| author_role | aut |
| author_sort | Isakov, Victor 1947- |
| author_variant | v i vi |
| building | Verbundindex |
| bvnumber | BV004291402 |
| classification_rvk | SK 560 |
| classification_tum | MAT 350f |
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| dewey-full | 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004291402 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:11:02Z |
| institution | BVB |
| isbn | 0821815326 9780821815328 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002669571 |
| oclc_num | 243446950 |
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| owner_facet | DE-384 DE-91G DE-BY-TUM DE-12 DE-355 DE-BY-UBR DE-29T DE-83 DE-11 DE-188 DE-20 |
| physical | xiv, 193 Seiten |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Isakov, Victor 1947- Verfasser (DE-588)118129570 aut Inverse source problems Victor Isakov Providence, Rhode Island American Mathematical Society [1990] © 1990 xiv, 193 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Number 34 Inverses Problem (DE-588)4125161-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 s Inverses Problem (DE-588)4125161-1 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Erscheint auch als Online-Ausgabe 978-1-4704-1261-6 Mathematical surveys and monographs Number 34 (DE-604)BV000018014 34 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002669571&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Isakov, Victor 1947- Inverse source problems Mathematical surveys and monographs Inverses Problem (DE-588)4125161-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Potenzialtheorie (DE-588)4046939-6 gnd |
| subject_GND | (DE-588)4125161-1 (DE-588)4044779-0 (DE-588)4046939-6 |
| title | Inverse source problems |
| title_auth | Inverse source problems |
| title_exact_search | Inverse source problems |
| title_full | Inverse source problems Victor Isakov |
| title_fullStr | Inverse source problems Victor Isakov |
| title_full_unstemmed | Inverse source problems Victor Isakov |
| title_short | Inverse source problems |
| title_sort | inverse source problems |
| topic | Inverses Problem (DE-588)4125161-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Potenzialtheorie (DE-588)4046939-6 gnd |
| topic_facet | Inverses Problem Partielle Differentialgleichung Potenzialtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002669571&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT isakovvictor inversesourceproblems |