Inverse problems in differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York ; London
Plenum Press
[1990]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 227 - 249 |
| Beschreibung: | 255 Seiten Diagramme |
| ISBN: | 0306431645 |
Internformat
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| 100 | 1 | |a Anger, Gottfried |d 1928- |0 (DE-588)1063115094 |4 aut | |
| 245 | 1 | 0 | |a Inverse problems in differential equations |c Gottfried Anger: Department of Mathematics, Martin Luther University Halle - Wittenberg, German Democratic Republie |
| 264 | 1 | |a New York ; London |b Plenum Press |c [1990] | |
| 264 | 4 | |c © 1990 | |
| 300 | |a 255 Seiten |b Diagramme | ||
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| 500 | |a Literaturverz. S. 227 - 249 | ||
| 650 | 4 | |a Partielle Differentialgleichung - Inverses Problem | |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
On the interpretation of nature 9
1. Some special inverse problems on the real line 14
1.1. Some remarks on the set of real numbers 14
1.2. The Abel integral equation 14
1.3. Some special differential equations of the first order 26
1.4. Differential equations of the second order 32
1.5. Inverse spectral problems 35
1.6. Differential equations of higher order 36
1.7. Consequences for the theory of inverse problems 37
2. Actual differential equations in applications 40
2.1. The Laplace equation and elliptic differential equations of second order . 40
2.2. Heat equation and parabolic differential equations of second order ... 49
2.3. Wave equation and hyperbolic differential equations of second order . . 58
2.4. Systems of partial differential equations 63
2.5. Equations of higher order 64
3. Potentials 66
3.1. Classical potentials 66
3.2. Some uniqueness theorems for classical potentials 75
3.3. Some remarks on integration theory 80
3.4. Potentials, continuous potentials, C capacity 91
4. The space of continuous functions in inverse problems 105
4.1. A new transformation 105
4.2. The balayage principle as projection on the dual space of the space of con¬
tinuous functions 109
4.3. Approximation theorems 115
4.4. A general form of the balayage principle 125
5. Inverse source problems 132
5.1. Some special inverse source problems in 1R1 132
5.2. Some special extremal elements of S$( 5X») 136
5.3. General theorems on inverse source problems 144
5.4. The geometrical interpretation of extremal measures 149
5.5. The case of a harmonic density. Analytic continuation of special potentials 160
5.6. An inverse source problem for the heat equation 174
6. Some one dimensional inverse problems in differential equations 190
6.1. Explicitly solvable inverse problems in heat conduction 190
8 Contents
6.2. A nonlinear inverse problem in which the coefficients depend on the gra¬
dient of the solution 194
7. Some inverse problems for nonlinear equations 204
7.1. A uniqueness theorem for determining conductivity from overspecified data 204
7.2. A nonlinear parabolic inverse coefficient problem 210
8. Global uniqueness theorems for linear differential equations 216
9. Some historical remarks 222
Conclusions 225
References 227
Symbol Index 250
Subject Index 252
|
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| classification_rvk | SK 540 SK 560 |
| classification_tum | MAT 341f |
| ctrlnum | (OCoLC)246726014 (DE-599)BVBBV003594157 |
| discipline | Mathematik |
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| id | DE-604.BV003594157 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:02:27Z |
| institution | BVB |
| isbn | 0306431645 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002288572 |
| oclc_num | 246726014 |
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| owner_facet | DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-706 DE-83 DE-188 DE-20 |
| physical | 255 Seiten Diagramme |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Plenum Press |
| record_format | marc |
| spelling | Anger, Gottfried 1928- (DE-588)1063115094 aut Inverse problems in differential equations Gottfried Anger: Department of Mathematics, Martin Luther University Halle - Wittenberg, German Democratic Republie New York ; London Plenum Press [1990] © 1990 255 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 227 - 249 Partielle Differentialgleichung - Inverses Problem Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 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=002288572&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Anger, Gottfried 1928- Inverse problems in differential equations Partielle Differentialgleichung - Inverses Problem Differentialgleichung (DE-588)4012249-9 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4125161-1 |
| title | Inverse problems in differential equations |
| title_auth | Inverse problems in differential equations |
| title_exact_search | Inverse problems in differential equations |
| title_full | Inverse problems in differential equations Gottfried Anger: Department of Mathematics, Martin Luther University Halle - Wittenberg, German Democratic Republie |
| title_fullStr | Inverse problems in differential equations Gottfried Anger: Department of Mathematics, Martin Luther University Halle - Wittenberg, German Democratic Republie |
| title_full_unstemmed | Inverse problems in differential equations Gottfried Anger: Department of Mathematics, Martin Luther University Halle - Wittenberg, German Democratic Republie |
| title_short | Inverse problems in differential equations |
| title_sort | inverse problems in differential equations |
| topic | Partielle Differentialgleichung - Inverses Problem Differentialgleichung (DE-588)4012249-9 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Partielle Differentialgleichung - Inverses Problem Differentialgleichung Inverses Problem |
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