Ill-posed problems of mathematical physics and analysis:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1986
|
| Schriftenreihe: | Translations of mathematical monographs
64 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | EST: Nekorrektnye zadači matematičeskoj fiziki i analiza <engl.>. - Aus d. Russ. übers. |
| Beschreibung: | VI, 290 S. |
| ISBN: | 0821845179 |
Internformat
MARC
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| 100 | 1 | |a Lavrentʹev, Michail Michajlovič |d 1932-2010 |e Verfasser |0 (DE-588)135733200 |4 aut | |
| 240 | 1 | 0 | |a Nekorrektnye zadači matematičeskoj fiziki i analiza |
| 245 | 1 | 0 | |a Ill-posed problems of mathematical physics and analysis |c by M. M. Lavrent'ev ; V. G. Romanov ; S. P. Shishatskii |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1986 | |
| 300 | |a VI, 290 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 64 | |
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| 650 | 4 | |a Physique mathématique | |
| 650 | 4 | |a Problèmes aux limites - Problèmes mal posés | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Boundary value problems |x Improperly posed problems | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Numerical analysis |x Improperly posed problems | |
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Datensatz im Suchindex
| _version_ | 1804115099166703616 |
|---|---|
| adam_text | Contents
Preface v
Introduction 1
CHAPTER I. Physical Formulations Leading to Ill posed Problems 7
1. Continuation of static fields 7
2. Problems for the diffusion equation 10
3. Continuation of fields from discrete sets 11
4. Processing readings of physical instruments 13
5. Inverse problems of geophysics 15
6. Inverse problems of gravimetry 16
7. The inverse kinematic problem of seismology 19
CHAPTER II. Basic Concepts of the Theory of Ill posed Problems 26
1. Problems well posed in the Tikhonov sense 26
2. Regularization 32
3. Linear ill posed problems 39
CHAPTER III. Analytic Continuation 48
1. Formulations of problems and classical results 48
2. Analytic continuation from continua 52
3. Analytic continuation from classes of sets including discrete sets 57
4. Recovery of solutions of elliptic and parabolic equations from
their values on sets lying inside the domain of regularity 63
CHAPTER IV. Boundary Value Problems for Differential Equations 72
1. The noncharacteristic Cauchy problem for a parabolic equation.
The Cauchy problem for an elliptic equation 73
2. A mixed problem for a parabolic equation with decreasing time 95
3. Cauchy problems with data on a segment of the time axis for
degenerate parabolic and pseudoparabolic equations 106
iii
iv CONTENTS
4. Cauchy problems with data on a timelike surface for hyperbolic
and ultrahyperbolic equations 123
CHAPTER V. Volterra Equations 155
1. Regularization of a Volterra equation of the first kind 155
2. Operator Volterra equations of the first kind 159
CHAPTER VI. Integral Geometry 168
1. The problem of finding a function from its spherical means 170
2. Problems of integral geometry on a family of manifolds which is
invariant under a group of transformations of the space 175
3. Integral geometry in special classes of functions 183
4. Integral geometry in the small 190
5. The problem of integral geometry in plane curves and energy
inequalities 202
CHAPTER VII. Multidimensional Inverse Problems for Linear
Differential Equations 209
1. Examples of formulations of multidimensional inverse problems.
Mathematical problems connected with investigating them 211
2. A general approach to investigating questions of uniqueness and
stability of inverse problems 220
3. Inverse problems for hyperbolic equations of second order 227
4. Inverse problems for first order hyperbolic systems 234
5. Inverse problems for parabolic equations of second order 251
1. The connection between solutions of direct problems for
equations of hyperbolic and parabolic types and inverse
problems 251
2. The method of descent in inverse problems 252
3. Inverse problems for equations of parabolic type 254
6. An abstract inverse problem and questions of its being well posed 255
1. Reduction to the investigation of a two parameter family of
linear equations 257
2. The method of linearization in investigating the inverse
problem 261
Bibliography 265
|
| any_adam_object | 1 |
| author | Lavrentʹev, Michail Michajlovič 1932-2010 Romanov, Vladimir G. Šišatskij, Sergej P. |
| author_GND | (DE-588)135733200 (DE-588)135734592 |
| author_facet | Lavrentʹev, Michail Michajlovič 1932-2010 Romanov, Vladimir G. Šišatskij, Sergej P. |
| author_role | aut aut aut |
| author_sort | Lavrentʹev, Michail Michajlovič 1932-2010 |
| author_variant | m m l mm mml v g r vg vgr s p š sp spš |
| building | Verbundindex |
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| callnumber-search | QA3 QC20.7.B6 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 SK 950 |
| classification_tum | PHY 013f MAT 350f |
| ctrlnum | (OCoLC)13269365 (DE-599)BVBBV000651737 |
| dewey-full | 530.1/55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/55 |
| dewey-search | 530.1/55 |
| dewey-sort | 3530.1 255 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| genre | Unvollständige Problemstellung gnd |
| genre_facet | Unvollständige Problemstellung |
| id | DE-604.BV000651737 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:17:13Z |
| institution | BVB |
| isbn | 0821845179 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000406072 |
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| physical | VI, 290 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Lavrentʹev, Michail Michajlovič 1932-2010 Verfasser (DE-588)135733200 aut Nekorrektnye zadači matematičeskoj fiziki i analiza Ill-posed problems of mathematical physics and analysis by M. M. Lavrent'ev ; V. G. Romanov ; S. P. Shishatskii Providence, RI American Math. Soc. 1986 VI, 290 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 64 EST: Nekorrektnye zadači matematičeskoj fiziki i analiza <engl.>. - Aus d. Russ. übers. Analyse numérique - Problèmes mal posés Physique mathématique Problèmes aux limites - Problèmes mal posés Mathematische Physik Boundary value problems Improperly posed problems Mathematical physics Numerical analysis Improperly posed problems Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Unvollständige Problemstellung gnd rswk-swf Inkorrekt gestelltes Problem (DE-588)4186951-5 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Mathematische Physik (DE-588)4037952-8 s Randwertproblem (DE-588)4048395-2 s Unvollständige Problemstellung f 1\p DE-604 Romanov, Vladimir G. Verfasser (DE-588)135734592 aut Šišatskij, Sergej P. Verfasser aut Translations of mathematical monographs 64 (DE-604)BV000002394 64 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000406072&sequence=000002&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 | Lavrentʹev, Michail Michajlovič 1932-2010 Romanov, Vladimir G. Šišatskij, Sergej P. Ill-posed problems of mathematical physics and analysis Translations of mathematical monographs Analyse numérique - Problèmes mal posés Physique mathématique Problèmes aux limites - Problèmes mal posés Mathematische Physik Boundary value problems Improperly posed problems Mathematical physics Numerical analysis Improperly posed problems Partielle Differentialgleichung (DE-588)4044779-0 gnd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd Mathematische Physik (DE-588)4037952-8 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4186951-5 (DE-588)4037952-8 (DE-588)4048395-2 |
| title | Ill-posed problems of mathematical physics and analysis |
| title_alt | Nekorrektnye zadači matematičeskoj fiziki i analiza |
| title_auth | Ill-posed problems of mathematical physics and analysis |
| title_exact_search | Ill-posed problems of mathematical physics and analysis |
| title_full | Ill-posed problems of mathematical physics and analysis by M. M. Lavrent'ev ; V. G. Romanov ; S. P. Shishatskii |
| title_fullStr | Ill-posed problems of mathematical physics and analysis by M. M. Lavrent'ev ; V. G. Romanov ; S. P. Shishatskii |
| title_full_unstemmed | Ill-posed problems of mathematical physics and analysis by M. M. Lavrent'ev ; V. G. Romanov ; S. P. Shishatskii |
| title_short | Ill-posed problems of mathematical physics and analysis |
| title_sort | ill posed problems of mathematical physics and analysis |
| topic | Analyse numérique - Problèmes mal posés Physique mathématique Problèmes aux limites - Problèmes mal posés Mathematische Physik Boundary value problems Improperly posed problems Mathematical physics Numerical analysis Improperly posed problems Partielle Differentialgleichung (DE-588)4044779-0 gnd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd Mathematische Physik (DE-588)4037952-8 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Analyse numérique - Problèmes mal posés Physique mathématique Problèmes aux limites - Problèmes mal posés Mathematische Physik Boundary value problems Improperly posed problems Mathematical physics Numerical analysis Improperly posed problems Partielle Differentialgleichung Inkorrekt gestelltes Problem Randwertproblem Unvollständige Problemstellung |
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| volume_link | (DE-604)BV000002394 |
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