Inverse problems of wave processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Utrecht [u.a.]
VSP
2001
|
| Edition: | 1. publ. |
| Series: | Inverse and ill posed problems series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 133 - 137 |
| Physical Description: | 137 S. graph. Darst. : 25 cm |
| ISBN: | 9067643440 |
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| 100 | 1 | |a Blagoveščenskij, A. S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Inverse problems of wave processes |c A. S. Blagoveshchenskii |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Utrecht [u.a.] |b VSP |c 2001 | |
| 300 | |a 137 S. |b graph. Darst. : 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Inverse and ill posed problems series | |
| 500 | |a Literaturverz. S. 133 - 137 | ||
| 650 | 4 | |a Wave-motion, Theory of | |
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Record in the Search Index
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| adam_text | Contents
Introduction 1
Chapter 1. One dimensional inverse problems 9
1.1. Setting of a problem for string equation 9
1.1.1. General remarks 9
1.1.2. Mathematical setting of the problem 9
1.1.3. Physical interpretation of inverse problem data 10
1.1.4. Reformulation of the problem in terms of
a hyperbolic system 12
1.1.5. Determination of the string parameters from
a(y) and additional information 14
1.2. Peculiarities of solution. Formulation of the direct problem .... 15
1.2.1. Correct formulation of the direct problem 15
1.2.2. Singularities of solution of the hyperbolic system 19
1.2.3. Singularities of solution of the string equation 21
1.2.4. Singularities of solution in case of discontinuous
coefficients 22
1.3. The first method of solution of inverse problem 25
1.3.1. Derivation of the system of integral equations 25
1.3.2. Investigation of the system of integral equations 26
1.3.3. Continuous dependence of solution on inverse
problem data 30
1.3.4. Solution of the inverse problem by successive steps .... 31
1.3.5. The case of discontinuous a(y) 32
A.S. Blagoveshchenskii. Inverse Problems of Wave Processes
1.4. Method of linear integral equations 36
1.4.1. Fundamental system of solutions of equation (1.1.12) ... 36
1.4.2. Derivation of linear integral equations 37
1.4.3. Recovery of the coefficient q(y) from a solution of
the linear integral equation 40
1.4.4. Structure of equations (1.4.10). Existence and
uniqueness of solution 41
1.4.5. Modification of equations (1.4.14), (1.4.15) under
a change of the source 43
1.4.6. Proof of necessity. Conditions for solvability of
the inverse problem 44
1.4.7. Proof of sufficiency 46
1.5. The case of discontinuous cr(y) 47
1.5.1. The first method 47
1.5.2. The second method 48
1.6. The Gel fand Levitan equation for second order
hyperbolic equations 48
1.6.1. Derivation of a linear integral equation 48
1.6.2. Recovery of coefficients by solution of the
Gel fand Levitan equation 51
1.6.3. The scattering problem 52
1.7. Some cases of explicit solution
of inverse problem 53
1.7.1. Description of inverse problem data 53
1.7.2. Construction of the solution 54
1.8. On connection of inverse problems with nonlinear
ordinary differential equations 57
1.8.1. Connection between ordinary differential
equations and inverse problems 57
1.8.2. Use of the connection between differential
equations and inverse problems 59
1.9. The case of more general system of equations 63
1.9.1. Setting of a problem 63
1.9.2. Linear integral equations 64
1.9.3. Determination of q and 92 65
Contents
Chapter 2. Theory of inverse problems for wave
processes in layered media 67
2.1. Inverse problems of acoustics 67
2.1.1. General remarks 67
2.1.2. Setting of an inverse problem for the acoustic equation . . 68
2.1.3. Solving the inverse problem of acoustics by
the Fourier transformation 69
2.1.4. Solution of the inverse problem of acoustics
by the Radon transformation 71
2.1.5. The inverse problem of scattering a plane wave 74
2.1.6. The inverse problem of wave propagation in wave guides . 75
2.1.7. The inverse problem for a layered ball 77
2.1.8. The method of moments. Formulation of a problem and
its reduction to an integral equation 78
2.1.9. Construction of the Green function 80
2.1.10. Investigation of integral equation (2.1.34) 83
2.1.11. The inversion formula for the operator T 84
2.1.12. Once more about the scattering problem 86
2.2. General second order hyperbolic equation.
Problem in a half space 89
2.2.1. Setting of a problem 89
2.2.2. Transformation of the problem 90
2.3. The scattering problem for the general hyperbolic equation .... 92
2.3.1. Setting of the problem, reformulation in terms
of a system 92
2.3.2. Reduction to an inverse problem investigated above .... 94
2.3.3. The maximum possible information on the
coefficients of equation (2.2.1) 96
Chapter 3. Inverse problems for vector wave processes 99
3.1. Inverse problem for elasticity equation 99
3.1.1. General remarks 99
3.1.2. Setting of the problem 99
3.1.3. Solution of the inverse Lamb problem 100
A.S. Blagoveshchenskii. Inverse Problems of Wave Processes
3.2. Inverse problem of sound propagation in
a moving layered medium 103
3.2.1. Acoustic equations in a moving medium 103
3.2.2. Transformation of the system for the layered medium . . . 104
3.3. The case of one dimensional sound propagation 108
3.3.1. General description of the problems in question 108
3.3.2. Mathematical setting of the problems 109
3.3.3. Formulation of the results 111
3.3.4. Integral equations for Problem 1 111
3.3.5. Integral equations for Problem 2 114
3.3.6. The model problem 115
3.4. Inverse problems for hyperbolic systems 117
3.4.1. General remarks. Setting of a problem 117
3.4.2. Formulation of the direct problem 118
3.4.3. Setting of the inverse problem. Formulation of the result . 120
3.4.4. Proof 120
3.5. Second order hyperbolic system 122
3.5.1. Setting of a problem 122
3.5.2. Proof 123
3.5.3. The inverse problem with a fixed interval of
nonhomogeneities 130
Bibliography 133
|
| any_adam_object | 1 |
| author | Blagoveščenskij, A. S. |
| author_facet | Blagoveščenskij, A. S. |
| author_role | aut |
| author_sort | Blagoveščenskij, A. S. |
| author_variant | a s b as asb |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 560 |
| ctrlnum | (OCoLC)47078020 (DE-599)BVBBV013748058 |
| dewey-full | 530.12/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12/4 |
| dewey-search | 530.12/4 |
| dewey-sort | 3530.12 14 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:51:18Z |
| institution | BVB |
| isbn | 9067643440 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009398057 |
| oclc_num | 47078020 |
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| owner | DE-703 |
| owner_facet | DE-703 |
| physical | 137 S. graph. Darst. : 25 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | VSP |
| record_format | marc |
| series2 | Inverse and ill posed problems series |
| spelling | Blagoveščenskij, A. S. Verfasser aut Inverse problems of wave processes A. S. Blagoveshchenskii 1. publ. Utrecht [u.a.] VSP 2001 137 S. graph. Darst. : 25 cm txt rdacontent n rdamedia nc rdacarrier Inverse and ill posed problems series Literaturverz. S. 133 - 137 Wave-motion, Theory of Wellengleichung (DE-588)4065315-8 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 s Wellengleichung (DE-588)4065315-8 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=009398057&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blagoveščenskij, A. S. Inverse problems of wave processes Wave-motion, Theory of Wellengleichung (DE-588)4065315-8 gnd Wellenausbreitung (DE-588)4121912-0 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4065315-8 (DE-588)4121912-0 (DE-588)4125161-1 |
| title | Inverse problems of wave processes |
| title_auth | Inverse problems of wave processes |
| title_exact_search | Inverse problems of wave processes |
| title_full | Inverse problems of wave processes A. S. Blagoveshchenskii |
| title_fullStr | Inverse problems of wave processes A. S. Blagoveshchenskii |
| title_full_unstemmed | Inverse problems of wave processes A. S. Blagoveshchenskii |
| title_short | Inverse problems of wave processes |
| title_sort | inverse problems of wave processes |
| topic | Wave-motion, Theory of Wellengleichung (DE-588)4065315-8 gnd Wellenausbreitung (DE-588)4121912-0 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Wave-motion, Theory of Wellengleichung Wellenausbreitung Inverses Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009398057&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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