Inverse problems for partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; Berlin [u.a.]
Springer
1998
|
| Series: | Applied mathematical sciences
127 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 284 S. graph. Darst. |
| ISBN: | 0387982566 |
Staff View
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Record in the Search Index
| _version_ | 1804126321762107392 |
|---|---|
| adam_text | VICTOR ISAKOV
INVERSE PROBLEMS
FOR PARTIAL
DIFFERENTIAL EQUATIONS
SPRINGER
CONTENTS
PREFACE VII
CHAPTER 1 INVERSE PROBLEMS 1
1.1 THE INVERSE PROBLEM OF GRAVIMETRY 1
1.2 THE INVERSE CONDUCTIVITY PROBLEM 5
.
1.3 INVERSE SCATTERING 7
1.4 TOMOGRAPHY AND THE INVERSE SEISMIC PROBLEM 10
1.5 INVERSE SPECTRAL PROBLEMS 14
CHAPTER 2 ILL-POSED PROBLEMS AND REGULARIZATION 20
2.1 WELL-AN
D ILL-POSED PROBLEMS 20
2.2 CONDITIONAL CORRECTNESS. REGULARIZATION 23
2.3 CONSTRUCTION OF REGULARIZE
S 26
2.4 CONVERGENCE OF REGULARIZATION ALGORITHMS 32
2.5 ITERATIVE ALGORITHMS 36
CHAPTER 3 UNIQUENESS AND STABILITY IN THE CAUCHY PROBLEM 39
3.1 THE BACKWARD PARABOLIC EQUATION 39
3.2 GENERAL CARLEMAN TYPE ESTIMATES AND THE CAUCHY PROBLEM 48
3.3 ELLIPTIC AND PARABOLIC EQUATIONS 53
3.4 HYPERBOLIC AND SCHRODINGER EQUATIONS 59
3.5 OPEN PROBLEMS 71
CHAPTER 4 ELLIPTIC EQUATIONS: SINGLE BOUNDARY MEASUREMENTS 73
4.0 RESULTS ON ELLIPTIC BOUNDARY VALUE PROBLEMS 73
4.1 INVERSE GRAVIMETRY 76
4.2 RECONSTRUCTION OF LOWER-ORDER TERMS 81
4.3 THE INVERSE CONDUCTIVITY PROBLEM 85
4.4 METHODS OF THE THEORY OF ONE COMPLEX VARIABLE 93
4.5 LINEARIZATION OF THE COEFFICIENTS PROBLEM 98
4.6 SOME PROBLEMS OF NONDESTRUCTIVE EVALUATION 100
4.7 OPEN PROBLEMS 103
IX
CONTENTS
CHAPTER 5 ELLIPTIC EQUATIONS: MANY BOUNDARY MEASUREMENTS
5.0 THE DIRICHLET-TO-NEUMANN MAP
5.1 BOUNDARY RECONSTRUCTION
5.2.RECONSTRUCTION IN
2
5.3 COMPLETENESS OF PRODUCTS OF SOLUTIONS OF PDE
5.4 THE PLANE CASE
5.5 RECOVERY OF SEVERAL COEFFICIENTS
5.6 NONLINEAR EQUATIONS
5.7 DISCONTINUOUS CONDUCTIVITIES
5.8 MAXWELL S AND ELASTICITY SYSTEMS
5.9 OPEN PROBLEMS
CHAPTER 6 SCATTERING PROBLEMS
6.0 DIRECT SCATTERING
6.1 FROM
A
TO NEAR FIELD
6.2 SCATTERING BY A MEDIUM
6.3 SCATTERING BY OBSTACLES
6.4 OPEN PROBLEMS
CHAPTER 7 INTEGRAL GEOMETRY AND TOMOGRAPHY
7.1 THE RADON TRANSFORM AND ITS INVERSE
7.2 THE ENERGY INTEGRALS METHODS
7.3 BOMAN S COUNTEREXAMPLE
7.4 THE TRANSPORT EQUATION
7.5 OPEN PROBLEMS
CHAPTER 8 HYPERBOLIC EQUATIONS
8.0 INTRODUCTION
8.1 THE ONE-DIMENSIONAL CASE
8.2 SINGLE BOUNDARY MEASUREMENTS
8.3 MANY MEASUREMENTS: USE OF BEAM SOLUTIONS
8.4 MANY MEASUREMENTS: METHODS OF BOUNDARY CONTROL
8.5 RECOVERY OF DISCONTINUITY OF THE SPEED OF PROPAGATION
8.6 OPEN PROBLEMS
CHAPTER 9 PARABOLIC EQUATIONS
9.0 INTRODUCTION
9.1 FINAL OVERDETERMINATION
9.2 LATERAL OVERDETERMINATION: SINGLE MEASUREMENTS
9.3 LATERAL OVERDETERMINATION: MANY MEASUREMENTS
9.4 DISCONTINUOUS PRINCIPAL COEFFICIENT
9.5 NONLINEAR EQUATIONS
9.6 INTERIOR SOURCES
9.7 OPEN PROBLEMS
105
105
108
112
114
118
121
127
131
137
141
144
144
147
151
155
161
163
163
172
175
179
181
184
184
187
195
199
205
211
215
217
217
220
226
228
232
237
242
244
CONTENTS XI
CHAPTER 10 SOME NUMERICAL METHODS 246
10.1 LINEARIZATION 247
10.2 VARIATIONAL REGULARIZATION OF THE CAUCHY PROBLEM 252
10.3 RELAXATION METHODS 256
10.4 LAYER-STRIPPING 258
10.5 DISCRETE METHODS 261
APPENDIX. FUNCTIONAL SPACES 265
REFERENCES 269
INDEX 283
|
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| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV011778581 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:15:36Z |
| institution | BVB |
| isbn | 0387982566 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007949283 |
| oclc_num | 845435179 |
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| owner_facet | DE-20 DE-703 DE-29T DE-824 DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 |
| physical | XI, 284 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| 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 New York ; Berlin [u.a.] Springer 1998 XI, 284 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 127 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 DE-604 Applied mathematical sciences 127 (DE-604)BV000005274 127 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007949283&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Isakov, Victor 1947- Inverse problems for partial differential equations Applied mathematical sciences 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 | Inverses Problem (DE-588)4125161-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Inverses Problem Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007949283&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT isakovvictor inverseproblemsforpartialdifferentialequations |