Inverse problems for partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham
Springer
2017
|
| Edition: | Third edition |
| Series: | Applied mathematical sciences
Volume 127 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 406 Seiten |
| ISBN: | 9783319516578 |
Staff View
MARC
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| 650 | 4 | |a Partial differential equations | |
| 650 | 4 | |a Computer mathematics | |
| 650 | 4 | |a Physics | |
| 650 | 4 | |a Partial Differential Equations | |
| 650 | 4 | |a Computational Mathematics and Numerical Analysis | |
| 650 | 4 | |a Theoretical, Mathematical and Computational Physics | |
| 650 | 4 | |a Remote Sensing/Photogrammetry | |
| 650 | 4 | |a Mathematik | |
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Record in the Search Index
| _version_ | 1804177407708495872 |
|---|---|
| adam_text | Titel: Inverse problems for partial differential equations
Autor: Isakov, Victor
Jahr: 2017
Contents
Preface to the Third Edition....................................................................vii
Preface to the Second Edition................................................................ix
Preface to the First Edition ....................................................................xi
Chapter 1 Inverse Problems................................................................1
1.1 The Inverse Problem of Gravimetry............................1
1.2 The Inverse Conductivity Problem..............................6
1.3 Inverse Scattering..........................................................8
1.4 Tomography and the Inverse Seismic Problem..........12
1.5 Inverse Spectral Problems............................................16
Chapter 2 III-Posed Problems and Regularization......................23
2.1 Well- and 111-Posed Problems......................................23
2.2 Conditional Correctness: Regularization....................27
2.3 Construction of Regularizers........................................30
2.4 Convergence of Regularization Algorithms................37
2.5 Iterative Algorithms......................................................42
Chapter 3 Uniqueness and Stability in the Cauchy
Problem..................................................................................47
3.1 The Backward Parabolic Equation..............................48
3.2 General Carleman Estimates and the Cauchy
Problem............................................................................58
3.3 Elliptic and Parabolic Equations................................65
3.4 Hyperbolic and Schrödinger Equations......................73
3.5 Systems of Partial Differential Equations..................95
3.6 Open Problems ...............................101
xiii
xiv Contents
Chapter 4 Elliptic Equations: Single Boundary
Measurements...................................105
4.0 Results on Elliptic Boundary Value Problems.....105
4.1 Inverse Gravimetry............................108
4.2 Reconstruction of Lower-Order Terms............114
4.3 The Inverse Conductivity Problem...............119
4.4 Methods of the Theory of One Complex Variable .. 130
4.5 Linearization of the Coefficient Problem..........135
4.6 Some Problems of Detection of Defects...........139
4.7 Open Problems ...............................146
Chapter 5 Elliptic Equations: Many Boundary
Measurements...................................149
5.0 The Dirichlet-to-Neumann Map and the
Cauchy Set...................................149
5.1 Boundary Reconstruction.......................154
5.2 Completeness of Products of Solutions of PDE .... 159
5.3 Uniqueness and Stability in Q...................165
5.4 Recovery of Several Coefficients.................172
5.5 The Plane Case...............................178
5.6 Nonlinear Equations...........................186
5.7 Transmission Problems.........................193
5.8 Maxwell s and Elasticity Systems................202
5.9 Open Problems ...............................208
Chapter 6 Scattering Problems and Stationary Waves......211
6.0 Direct Scattering..............................211
6.1 From A to Near Field..........................214
6.2 The Inverse Source Problem with Many Wave
Numbers.....................................222
6.3 Scattering by a Medium........................225
6.4 Scattering by Obstacles........................231
6.5 Open Problems ...............................238
Chapter 7 Integral Geometry and Tomography.............241
7.1 The Radon Transform and its Inverse............241
7.2 The Energy Integral Methods...................251
7.3 Boman s Counterexample.......................255
7.4 The Transport Equation........................259
7.5 Open Problems ...............................266
Chapter 8 Hyperbolic Problems............................269
8.0 Introduction..................................269
8.1 The One-Dimensional Case.....................273
8.2 Single Boundary Measurements .................281
8.3 Many Measurements: The Use of Beam Solutions .. 290
Contents xv
8.4 Many measurements: Methods of Boundary
Control ......................................296
8.5 Recovery of Discontinuity of the Speed
of Propagation................................303
8.6 Open Problems ...............................307
Chapter 9 Inverse Parabolic Problems......................309
9.0 Introduction..................................309
9.1 Final Overdetermination.......................313
9.2 Lateral Overdetermination: Single Measurements .. 319
9.3 The Inverse Problem of Option Pricing...........325
9.4 Lateral Overdetermination: Many Measurements .. 331
9.5 Discontinuous Principal Coefficient and Recovery
of a Domain..................................335
9.6 Nonlinear Equations...........................345
9.7 Interior Sources...............................350
9.8 Open Problems ...............................352
Chapter 10 Some Numerical Methods .......................355
10.1 Numerics for the Cauchy Problem...............356
10.2 Linearization..................................362
10.3 Relaxation Methods ...........................367
10.4 Layer Stripping ...............................370
10.5 Range Test Algorithms.........................373
10.6 Discrete Methods..............................377
Appendix. Function Spaces...................................381
References....................................................385
Index.........................................................405
|
| 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 | BV044244181 |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)982133381 (DE-599)BVBBV044244181 |
| 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 | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Third edition |
| format | Book |
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| id | DE-604.BV044244181 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:47:35Z |
| institution | BVB |
| isbn | 9783319516578 |
| language | English |
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| physical | xv, 406 Seiten |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Isakov, Victor 1947- Verfasser (DE-588)118129570 aut Inverse problems for partial differential equations Victor Isakov Third edition Cham Springer 2017 © 2017 xv, 406 Seiten txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences Volume 127 Mathematics Remote sensing Partial differential equations Computer mathematics Physics Partial Differential Equations Computational Mathematics and Numerical Analysis Theoretical, Mathematical and Computational Physics Remote Sensing/Photogrammetry Mathematik Inverses Problem (DE-588)4125161-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Inverses Problem (DE-588)4125161-1 s 1\p DE-604 Erscheint auch als Online-Ausgabe 978-3-319-51658-5 (DE-604)BV044206325 Applied mathematical sciences Volume 127 (DE-604)BV000005274 127 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029649434&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Isakov, Victor 1947- Inverse problems for partial differential equations Applied mathematical sciences Mathematics Remote sensing Partial differential equations Computer mathematics Physics Partial Differential Equations Computational Mathematics and Numerical Analysis Theoretical, Mathematical and Computational Physics Remote Sensing/Photogrammetry Mathematik Inverses Problem (DE-588)4125161-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4125161-1 (DE-588)4044779-0 |
| title | Inverse problems for partial differential equations |
| title_auth | Inverse problems for partial differential equations |
| title_exact_search | Inverse problems for partial differential equations |
| title_full | Inverse problems for partial differential equations Victor Isakov |
| title_fullStr | Inverse problems for partial differential equations Victor Isakov |
| title_full_unstemmed | Inverse problems for partial differential equations Victor Isakov |
| title_short | Inverse problems for partial differential equations |
| title_sort | inverse problems for partial differential equations |
| topic | Mathematics Remote sensing Partial differential equations Computer mathematics Physics Partial Differential Equations Computational Mathematics and Numerical Analysis Theoretical, Mathematical and Computational Physics Remote Sensing/Photogrammetry Mathematik Inverses Problem (DE-588)4125161-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Mathematics Remote sensing Partial differential equations Computer mathematics Physics Partial Differential Equations Computational Mathematics and Numerical Analysis Theoretical, Mathematical and Computational Physics Remote Sensing/Photogrammetry Mathematik Inverses Problem Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029649434&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT isakovvictor inverseproblemsforpartialdifferentialequations |