Identification problems of wave phenomena: theory and numerics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Utrecht, The Netherlands
VSP
1999
|
| Edition: | 1. publ. |
| Series: | Inverse and ill-posed problems series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 342 S. |
| ISBN: | 9067643157 |
Staff View
MARC
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| 245 | 1 | 0 | |a Identification problems of wave phenomena |b theory and numerics |c S. I. Kabanikhin and A. Lorenzi |
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| 264 | 1 | |a Utrecht, The Netherlands |b VSP |c 1999 | |
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Record in the Search Index
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| adam_text | IMAGE 1
INVERSE AND ILL-POSED PROBLEMS SERIES
IDENTIFICATION
PROBLEMS OF WAVE PHENOMENA
THEORY AND NUMERICS
S.L. KABANIKHIN ANDA. LORENZI
///VSP/// UTRECHT, THE NETHERLANDS, 1999
IMAGE 2
CONTENTS
INTRODUCTION IX
CHAPTER 1. STATEMENTS OF THE DIRECT AND INVERSE PROBLEMS. EXAMPLES 1
1.1. INTRODUCTION 1
1.2. INVERSE PROBLEMS OF MATHEMATICAL PHYSICS 3
1.3. INVERSE PROBLEM FOR THE WAVE EQUATION 4
1.4. THE EQUATION OF PLANE WAVES. THE D ALEMBERT FORMULA 7
1.5. THE CAUCHY PROBLEM 9
1.6. THE D ALEMBERT OPERATOR WITH SMOOTH INITIAL DATA 10
1.7. THE KIRCHHOFF AND POISSON FORMULAE 13
1.8. HUYGENS PRINCIPLE 15
1.9. TIME-LIKE AND SPACE-LIKE SURFACES 15
1.10. INVERSE PROBLEMS WITH SMOOTH INITIAL DATA 20
1.11. INVERSE PROBLEM FOR THE ACOUSTIC EQUATION 30
CHAPTER 2. VOLTERRA OPERATOR EQUATIONS 35
2.1. MAIN DEFMITIONS 35
2.2. LOCAL WELL-POSEDNESS 37
2.3. WELL-POSEDNESS FOR SUFFICIENTLY SMALL DATA 40
2.4. WELL-POSEDNESS IN THE NEIGHBORHOOD OF THE EXACT SOLUTION 44
CHAPTER 3. INVERSE PROBLEMS FOR MAXWELL S EQUATIONS 47
3.1. INTRODUCTION 47
3.2. REDUCTION OF INVERSE PROBLEM FOR MAXWELL S EQUATIONS TO A VOLTERRA
OPERATOR EQUATION 57
IMAGE 3
VI S. I. KAHANIKHIN AND A. LORENZI. IDENTIFICATION PROBLEMS ...
3.3. LOCAL WELL-POSEDNESS AND GLOBAL UNIQUENESS 59
3.4. WELL-POSEDNESS IN THE NEIGHBORHOOD OF THE EXACT SOLUTION 62
CHAPTER 4. LINEARIZATION AND NEWTON - KANTOROVICH METHOD 67
4.1. LINEARIZATION OF VOLTERRA OPERATOR EQUATIONS 67
4.2. THE LINEARIZED INVERSE PROBLEM FOR THE WAVE EQUATION 70
4.3. THE NEWTON - KANTOROVICH METHOD 80
CHAPTER 5. THE GEL FAND - LEVITAN METHOD 87
5.1. INTRODUCTION 87
5.2. GEL FAND-LEVITAN S APPROACH TO MULTIDIMENSIONAL INVERSE
PROBLEMS 90
5.3. DISCRETE INVERSE PROBLEMS 95
5.4. DISCRETE DIRECT PROBLEMS 98
5.5. AN AUXILIARY PROBLEM 101
5.6. A NECESSARY CONDITION FOR THE EXISTENCE OF THE GLOBAL SOLUTION TO
THE DISCRETE INVERSE PROBLEM 109
5.7. SUFFICIENT CONDITIONS FOR THE EXISTENCE OF THE GLOBAL SOLUTION TO
THE DISCRETE INVERSE PROBLEM 114
CHAPTER 6. REGULARIZATION 127
6.1. INTRODUCTION 127
6.2. VOLTERRA REGULARIZATION 131
CHAPTER 7. THE METHOD OF THE OPTIMAL CONTROL 137
7.1. INTRODUCTION 137
7.2. DISCRETE INVERSE PROBLEM 138
7.3. SPECIAL REPRESENTATION FOR THE SOLUTION TO THE DISCRETE DIRECT
PROBLEM 140
7.4. UNIQUENESS OF THE STATIONARY POINT 147
CHAPTER 8. INVERSION OF FINITE-DIFFERENCE SCHEMES 159
8.1. CONVERGENCE OF THE METHOD OF INVERSION OF FINITE-DIFFERENCE SCHEMES
159
8.2. PICARD AND CARATHEODORY SUCCESSIVE APPROXIMATIONS 168
IMAGE 4
CONTENTS VII
CHAPTER 9. STRONGLY ILL-POSED PROBLEMS 171
9.1. A STRONGLY ILL-POSED PROBLEM FOR THE LAPLACE EQUATION 171
9.2. CONDITIONAL CONTINUOUS DEPENDENCE ON THE DATA 174
9.3. APPROXIMATE SOLUTIONS TO THE CAUCHY PROBLEM FOR THE LAPLACE
EQUATION 180
9.4. APPROXIMATE SOLUTIONS TO THE NON-CHARACTERISTIC PROBLEM FOR THE
MULTIDIMENSIONAL HEAT EQUATION 185
9.5. EXISTENCE OF SOLUTIONS SATISFYING OPERATOR INEQUALITIES 191
CHAPTER 10. IDENTIFICATION PROBLEMS RELATED TO FIRST-ORDER SCALAR
SEMILINEAR EQUATIONS 195
10.1. THE SCALAR INVERSE PROBLEM 195
CHAPTER 11. AN IDENTIFICATION PROBLEM FOR A FIRST-ORDER
INTEGRODIFFERENTIAL EQUATION 203
11.1. INTRODUCTION 204
11.2. THE IDENTIFICATION PROBLEM AND ITS EQUIVALENCE TO A SYSTEM OF
INTEGRAL EQUATIONS 204
11.3. EXISTENCE AND UNIQUENESS 211
11.4. PROOFOF LEMMA 11.2.1 214
CHAPTER 12. AN INVERSE HYPERBOLIC INTEGRO-DIFFERENTIAL PROBLEM ARISING
IN GEOPHYSICS. 217
12.1. INTRODUCTION AND STATEMENT OF THE MAIN RESULT 218
12.2. THE TRANSFORMED INVERSE PROBLEM 221
12.3. EQUIVALENCE OF PROBLEM (12.2.18)-(12.2.22) WITH A FIXED-POINT
SYSTEM 226
12.4. SOLVING THE FIXED-POINT SYSTEM (12.3.9)-(12.3.12) 228
12.5. ESTIMATING THE SOLUTION {Z,P,Q) TO PROBLEM (12.3.9)-(12.3.12) . .
232 12.6. PROOF OF THEOREM 12.1.1 236
CHAPTER 13. INTEGRO-DIFFERENTIAL IDENTIFICATION PROBLEMS RELATED TO THE
ONE-DIMENSIONAL WAVE EQUATION 237
13.1. INTRODUCTION 238
13.2. STATEMENT OF THE IDENTIFICATION PROBLEM 239
13.3. THE EXISTENCE AND UNIQUENESS THEOREM 248
IMAGE 5
VIII S. I. KABANIKHIN AND A. LORENZI. IDENTIFICATION PROBLEMS ...
CHAPTER 14. LAVRENT EV REGULARIZATION OF SOLUTIONS TO LINEAR
INTEGRO-DIFFERENTIAL INVERSE PROBLEMS 265
14.1. INTRODUCTION 265
14.2. WELL-POSEDNESS OF THE LINEAR INVERSE PROBLEM WHEN G 6 C 3 ([0, T])
270 14.3. A CONVERGENCE THEOREM 273
14.4. AN ALGORITHM FOR A NUMERICAL SOLUTION 278
14.5. BASIC PROPERTIES OF THE COST FUNCTION AND ITS GRADIENT 286
CHAPTER 15. A STABILITY RESULT FOR THE IDENTIFICATION OF A NON LINEAR
TERM IN A SEMILINEAR HYPERBOLIC INTEGRO-DIFFERENTIAL EQUATION 295
15.1. INTRODUCTION 295
15.2. STATEMENTS OF THE MAIN RESULTS 296
15.3. PROOF OF THEOREM 15.2.1 297
15.4. STATEMENT OF THE STABILITY RESULT 303
15.5. PROOF OF THEOREM 15.4.1 305
CHAPTER 16. INVERSE PROBLEMS IN ELECTROMAGNETOELASTICITY 309 16.1.
FORMULATION OF THE DIRECT AND INVERSE PROBLEMS 309
16.2. THE OPTIMIZATION METHOD FOR SOLVING THE INVERSE PROBLEM . . .. 312
16.3. THE FMITE-DIFFERENCE SCHEMES 319
BIBLIOGRAPHY 321
|
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| id | DE-604.BV016452645 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:10:40Z |
| institution | BVB |
| isbn | 9067643157 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010173177 |
| oclc_num | 43983765 |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | X, 342 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | VSP |
| record_format | marc |
| series2 | Inverse and ill-posed problems series |
| spelling | Kabanichin, S. I. Verfasser aut Identification problems of wave phenomena theory and numerics S. I. Kabanikhin and A. Lorenzi 1. publ. Utrecht, The Netherlands VSP 1999 X, 342 S. txt rdacontent n rdamedia nc rdacarrier Inverse and ill-posed problems series Inverse problems (Differential equations) Numerical solutions Wave-motion, Theory of Maxwellsche Gleichungen (DE-588)4221398-8 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Maxwellsche Gleichungen (DE-588)4221398-8 s Inverses Problem (DE-588)4125161-1 s DE-604 Lorenzi, Alfredo Sonstige oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010173177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kabanichin, S. I. Identification problems of wave phenomena theory and numerics Inverse problems (Differential equations) Numerical solutions Wave-motion, Theory of Maxwellsche Gleichungen (DE-588)4221398-8 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4221398-8 (DE-588)4125161-1 |
| title | Identification problems of wave phenomena theory and numerics |
| title_auth | Identification problems of wave phenomena theory and numerics |
| title_exact_search | Identification problems of wave phenomena theory and numerics |
| title_full | Identification problems of wave phenomena theory and numerics S. I. Kabanikhin and A. Lorenzi |
| title_fullStr | Identification problems of wave phenomena theory and numerics S. I. Kabanikhin and A. Lorenzi |
| title_full_unstemmed | Identification problems of wave phenomena theory and numerics S. I. Kabanikhin and A. Lorenzi |
| title_short | Identification problems of wave phenomena |
| title_sort | identification problems of wave phenomena theory and numerics |
| title_sub | theory and numerics |
| topic | Inverse problems (Differential equations) Numerical solutions Wave-motion, Theory of Maxwellsche Gleichungen (DE-588)4221398-8 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Inverse problems (Differential equations) Numerical solutions Wave-motion, Theory of Maxwellsche Gleichungen Inverses Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010173177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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