Inverse problems for partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer New York
[2006]
|
| Edition: | second edition |
| Series: | Applied mathematical sciences
Volume 127 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 344 Seiten Diagramme |
| ISBN: | 0387253645 9780387253640 |
Staff View
MARC
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| 100 | 1 | |a Isakov, Victor |d 1947- |0 (DE-588)118129570 |4 aut | |
| 245 | 1 | 0 | |a Inverse problems for partial differential equations |c Victor Isakov |
| 250 | |a second edition | ||
| 264 | 1 | |a New York, NY |b Springer New York |c [2006] | |
| 264 | 4 | |c © 2006 | |
| 300 | |a xiii, 344 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v Volume 127 | |
| 650 | 7 | |a Equações diferenciais parciais |2 larpcal | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Inverse problems (Differential equations) | |
| 650 | 0 | 7 | |a Inverses Problem |0 (DE-588)4125161-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
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| 259 | |a 12 | ||
Record in the Search Index
| _version_ | 1804133600925319168 |
|---|---|
| adam_text | Contents
Preface
to the Second Edition
vii
Preface to the First Edition
ix
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-and ill-posed problems
20
2.2
Conditional correctness: Regularization
23
2.3
Construction of regularizers
26
2.4
Convergence of regularization algorithms
33
2.5
Iterative algorithms
37
Chapter
3
Uniqueness and Stability in the Cauchy Problem
41
3.1
The backward parabolic equation
42
3.2
General
Carleman
estimates and the Cauchy problem
51
3.3
Elliptic and parabolic equations
57
3.4
Hyperbolic and
Schrödinger
equations
65
3.5
Systems of partial differential equations
80
3.6
Open problems
86
Chapter
4
Elliptic Equations: Single Boundary Measurements
89
4.0
Results on elliptic boundary value problems
89
4.1
Inverse gravimetry
92
4.2
Reconstruction of lower-order terms
97
4.3
The inverse conductivity problem
102
4.4
Methods of the theory of one complex variable
111
xii Contents
4.5
Linearization of the
coefficients
problem
116
4.6
Some problems of detection of defects
119
4.7
Open problems
125
Chapter
5
Elliptic Equations: Many Boundary Measurements
127
5.0
The Dirichlet-to-Neumann map
127
5.1
Boundary reconstruction
130
5.2
Reconstruction in
Ω
134
5.3
Completeness of products of solutions of PDE
138
5.4
Recovery of several coefficients
143
5.5
The plane case
149
5.6
Nonlinear equations
154
5.7
Discontinuous conductivities
160
5.8
Maxwell s and elasticity systems
166
5.9
Open problems
170
Chapter
6
Scattering Problems
173
6.0
Direct Scattering
173
6.1
From A to near field
176
6.2
Scattering by a medium
180
6.3
Scattering by obstacles
184
6.4
Open problems
190
Chapter
7
Integral Geometry and Tomography
192
7.1
The Radon transform and its inverse
192
7.2
The energy integral methods
201
7.3
Boman s counterexample
205
7.4
The transport equation
208
7.5
Open problems
215
Chapter
8
Hyperbolic Problems
218
8.0
Introduction
218
8.1
The one-dimensional case
221
8.2
Single boundary measurements
229
8.3
Many measurements: use of beam solutions
236
8.4
Many measurements: methods of boundary control
243
8.5
Recovery of discontinuity of the speed of propagation
249
8.6
Open problems
253
Chapter
9
Inverse parabolic problems
255
9.0
Introduction
255
9.1
Final overdetermination
259
9.2
Lateral overdetermination: single measurements
264
9.3
The inverse problem of option pricing
270
9.4
Lateral overdetermination: many measurements
275
Contents xiii
9.5
Discontinuous principal coefficient and recovery of a domain
279
9.6
Nonlinear equations
288
9.7
Interior sources
293
9.8
Open problems
295
Chapter
10
Some Numerical Methods
297
10.1
Linearization
298
10.2
Variational regularization of the Cauchy problem
303
10.3
Relaxation methods
308
10.4
Layer-stripping
310
10.5
Range test algorithms
ЗІЗ
10.6
Discrete methods
318
Appendix. Functional Spaces
321
References
324
Index
343
|
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| discipline | Allgemeine Naturwissenschaft Mathematik |
| edition | second edition |
| format | Book |
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| id | DE-604.BV020032742 |
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| indexdate | 2024-07-09T20:11:18Z |
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| isbn | 0387253645 9780387253640 |
| language | English |
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| spelling | Isakov, Victor 1947- (DE-588)118129570 aut Inverse problems for partial differential equations Victor Isakov second edition New York, NY Springer New York [2006] © 2006 xiii, 344 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences Volume 127 Equações diferenciais parciais larpcal Differential equations, Partial Inverse problems (Differential equations) 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 Erscheint auch als Online-Ausgabe 978-0-387-32183-7 Applied mathematical sciences Volume 127 (DE-604)BV000005274 127 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013353931&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 12 |
| spellingShingle | Isakov, Victor 1947- Inverse problems for partial differential equations Applied mathematical sciences Equações diferenciais parciais larpcal Differential equations, Partial Inverse problems (Differential equations) 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 | Equações diferenciais parciais larpcal Differential equations, Partial Inverse problems (Differential equations) Inverses Problem (DE-588)4125161-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Equações diferenciais parciais Differential equations, Partial Inverse problems (Differential equations) Inverses Problem Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013353931&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT isakovvictor inverseproblemsforpartialdifferentialequations |