Investigation methods for inverse problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Utrecht ; Boston ; Köln ; Tokyo
VSP
2002
|
| Edition: | 1. publ. |
| Series: | Inverse and ill posed problems series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 263 - 280 |
| Physical Description: | XII, 280 S. 25 cm |
| ISBN: | 9067643610 |
Staff View
MARC
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| 100 | 1 | |a Romanov, Vladimir G. |e Verfasser |0 (DE-588)135734592 |4 aut | |
| 245 | 1 | 0 | |a Investigation methods for inverse problems |c V. G. Romanov |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Utrecht ; Boston ; Köln ; Tokyo |b VSP |c 2002 | |
| 300 | |a XII, 280 S. |b 25 cm | ||
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| 490 | 0 | |a Inverse and ill posed problems series | |
| 500 | |a Literaturverz. S. 263 - 280 | ||
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Inverse problems (Differential equations) |x Numerical solutions | |
| 650 | 4 | |a Mathematical physics | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xi
1 Introduction 1
1.1 One dimensional inverse kinematics problem 3
1.2 Inverse dynamical problem for a string 8
1.3 Inverse problems for a layered medium 16
2 Ray statements of inverse problems 19
2.1 Posing of the inverse problems 19
2.2 Asymptotic expansion 21
2.2.1 Asymptotic expansion of the solution 21
2.2.2 Reduction of the inverse problem 23
2.2.3 Construction of r(x, y) 24
2.2.4 Proof of the expansion in the odd dimensional case . . 27
2.2.5 Proof of the expansion in the even dimensional case . . 33
2.2.6 Proof of the auxiliary lemma 35
2.3 Uniqueness theorems for the inverse problem 38
2.3.1 A proof of the stability estimate for the integral geom¬
etry problem 43
2.3.2 Uniqueness theorem for the integral geometry problem
related to a vector field 53
2.3.3 Proof of the uniqueness theorem for inverse
kinematics problem 59
2.3.4 The wave equation with an attenuation 61
2.3.5 Concluding remarks 62
2.4 Inverse problems related to a local heterogeneity 62
3 Local solvability of some inverse problems 69
3.1 Banach s spaces of analytic functions 70
3.2 Determining coefficients of the lower terms 71
3.2.1 Determining a coefficient of the lower term 71
vii
viii CONTENTS
3.2.2 Determining an attenuation coefficient 79
3.3 Determining the speed of the sound 82
3.4 A regularization method for solving an inverse problem .... 91
3.4.1 Theorems related to the system of integro differential
equations 95
3.4.2 Estimates of a solution to the algebraic equations . . . 102
3.4.3 Convergence the approximate solution to the exact one 110
4 Inverse problems with single measurements 121
4.1 Determining coefficient of the lowest term 122
4.1.1 Statement of the problem and stability estimates . . . 122
4.1.2 Proof of the stability theorems 124
4.1.3 Proof of Lemma 4.1.3 126
4.1.4 Proof of Lemma 4.1.4 130
4.2 Determining coefficients under first derivatives 136
4.3 Determining the speed of sound in the wave equation 141
4.3.1 Formulation of the problem and a stability estimate of
the solution 142
4.3.2 Proof of Theorem 4.3.1 144
4.3.3 Proof of Lemma 4.3.5 150
4.3.4 Proof of Lemma 4.3.6 155
4.3.5 Proof of the inequality (4.3.24) 162
4.4 Case of a point source 162
4.4.1 Formulations of the problem and results 163
4.4.2 Proofs of the stability theorems 164
4.4.3 Properties of a solution to problem (4.4.1) 167
4.4.4 Proof of Lemma 4.4.3 168
4.4.5 Proof of Lemma 4.4.4 170
5 Stability estimates related to inverse problems for the
transport equation 175
5.1 The problem of determining the relaxation and a density of
inner sources 176
5.1.1 Statement of basic and auxiliary problems 176
5.1.2 The basic results 179
5.1.3 Proof of Theorem 5.1.1 187
5.1.4 Proof of the auxiliary lemmas 194
5.2 A stability estimate in the problem of determining the disper¬
sion index and relaxation in 2D 201
5.2.1 Statement of the problem and the basic results 202
5.2.2 Proof of Lemma 5.2.1 206
CONTENTS ix
5.2.3 A priori estimates 208
5.2.4 Proof of Theorem 5.2.3 . 221
5.3 The problem of determining the dispersion index and
relaxation in 3D 224
5.3.1 Statement of the problem and the main results 224
5.3.2 Proof of Lemma 5.3.1 230
5.3.3 A priori estimates for function w{x, v) 232
5.3.4 Estimates for functions h{%, v) and 5{x) 234
5.3.5 A priori estimates and differential properties
of function u(x, u,u0). . 238
5.3.6 A priori estimates and properties
of function v(x, i/,v°) . . 241
5.3.7 Equations for the derivatives of function v(x, u, is0) . . 243
5.3.8 Proof of inequality (5.3.24) • 249
5.3.9 Proof of inequality (5.3.25) ¦ 251
5.3.10 Proof of inequality (5.3.26) 254
5.3.11 Auxiliary formulae 256
Bibliography 262
|
| any_adam_object | 1 |
| author | Romanov, Vladimir G. |
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| callnumber-subject | PR - English Literature |
| classification_rvk | SK 560 |
| ctrlnum | (OCoLC)50053010 (DE-599)BVBBV014331935 |
| dewey-full | 530.15/535 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15/535 |
| dewey-search | 530.15/535 |
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| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV014331935 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:01:50Z |
| institution | BVB |
| isbn | 9067643610 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009831957 |
| oclc_num | 50053010 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XII, 280 S. 25 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | VSP |
| record_format | marc |
| series2 | Inverse and ill posed problems series |
| spelling | Romanov, Vladimir G. Verfasser (DE-588)135734592 aut Investigation methods for inverse problems V. G. Romanov 1. publ. Utrecht ; Boston ; Köln ; Tokyo VSP 2002 XII, 280 S. 25 cm txt rdacontent n rdamedia nc rdacarrier Inverse and ill posed problems series Literaturverz. S. 263 - 280 Mathematische Physik Inverse problems (Differential equations) Numerical solutions Mathematical physics Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 s Inverses Problem (DE-588)4125161-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009831957&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Romanov, Vladimir G. Investigation methods for inverse problems Mathematische Physik Inverse problems (Differential equations) Numerical solutions Mathematical physics Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4131213-2 (DE-588)4125161-1 |
| title | Investigation methods for inverse problems |
| title_auth | Investigation methods for inverse problems |
| title_exact_search | Investigation methods for inverse problems |
| title_full | Investigation methods for inverse problems V. G. Romanov |
| title_fullStr | Investigation methods for inverse problems V. G. Romanov |
| title_full_unstemmed | Investigation methods for inverse problems V. G. Romanov |
| title_short | Investigation methods for inverse problems |
| title_sort | investigation methods for inverse problems |
| topic | Mathematische Physik Inverse problems (Differential equations) Numerical solutions Mathematical physics Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Mathematische Physik Inverse problems (Differential equations) Numerical solutions Mathematical physics Hyperbolische Differentialgleichung Inverses Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009831957&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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