Abstract Cauchy problems: three approaches
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2001
|
| Schriftenreihe: | Chapman & Hall CRC monographs and surveys in pure and applied mathematics
120 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXI, 236 S. |
| ISBN: | 1584882506 |
Internformat
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Datensatz im Suchindex
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| adam_text | K CHAPMAN & HALL/CRC MONOGRAPHS AND SURVEYS IN PURE AND APPLIED
MATHEMATICS I 20 ABSTRACT CAUCHY PROBLEMS: THREE APPROACHES IRINAV.
MELNIKOVA ALEXEI FILINKOV CHAPMAN & HALL/CRC BOCA RATON LONDON NEW YORK
WASHINGTON, D.C. CONTENTS PREFACE XI INTRODUCTION XIII 0 ILLUSTRATION
AND MOTIVATION 1 0.1 HEAT EQUATION 1 0.2 THE REVERSED CAUCHY PROBLEM FOR
THE HEAT EQUATION 8 - 0.3 WAVE EQUATION 9 1 SEMIGROUP METHODS 17 1.1
CO-SEMIGROUPS 17 1.1.1 DEFINITIONS AND MAIN PROPERTIES 17 1.1.2 THE
CAUCHY PROBLEM 21 1.1.3 EXAMPLES 31 1.2 INTEGRATED SEMIGROUPS 34 1.2.1
EXPONENTIALLY BOUNDED INTEGRATED SEMIGROUPS . . . . 34 1.2.2 (N,
O;)-WELL-POSEDNESS OF THE CAUCHY PROBLEM . . . . 39 , - 1.2.3 LOCAL
INTEGRATED SEMIGROUPS 41 1.2.4 EXAMPLES 50 1.3 /T-CONVOLUTED SEMIGROUPS
54 1.3.1 GENERATORS OF K-CONVOLUTED SEMIGROUPS 54 1.3.2 0-CONVOLUTED
CAUCHY PROBLEM 59 1.4 C-REGULARIZED SEMIGROUPS 60 1.4.1 GENERATORS OF
C-REGULARIZED SEMIGROUPS 60 1.4.2 C-WELL-POSEDNESS OF THE CAUCHY PROBLEM
67 1.4.3 LOCAL C-REGULARIZED SEMIGROUPS 71 1.4.4 INTEGRATED SEMIGROUPS
AND C-REGULARIZED SEMIGROUPS 74 1.4.5 EXAMPLES 77 1.5 DEGENERATE
SEMIGROUPS 80 1.5.1 GENERATORS OF DEGENERATE SEMIGROUPS 80 VN VLLL 1.5.2
DEGENERATE 1-TIME INTEGRATED SEMIGROUPS 82 1.5.3 MAXIMAL CORRECTNESS
CLASS 86 1.5.4 (N,O;)-WELL-POSEDNESS OF A DEGENERATE CAUCHY PROBLEM 89
1.5.5 EXAMPLES 90 1.6 THE CAUCHY PROBLEM FOR INCLUSIONS 91 1.6.1
MULTIVALUED LINEAR OPERATORS 91 1.6.2 UNIFORM WELL-POSEDNESS 94 1.6.3
(N, W)-WELL-POSEDNESS 99 1.7 SECOND ORDER EQUATIONS 109 1.7.1 M,
TV-FUNCTIONS METHOD ILL 1.7.2 INTEGRATED SEMIGROUPS METHOD 114 1.7.3 THE
DEGENERATE CAUCHY PROBLEM 117 2 ABSTRACT DISTRIBUTION METHODS 121 2.1
THE CAUCHY PROBLEM 121 2.1.1 ABSTRACT (VECTOR-VALUED) DISTRIBUTIONS 121
2.1.2 WELL-POSEDNESS IN THE SPACE OF DISTRIBUTIONS 129 2.1.3
WELL-POSEDNESS IN THE SPACE OF EXPONENTIAL DISTRIBUTIONS 138 2.2 THE
DEGENERATE CAUCHY PROBLEM 142 2.2.1 A-ASSOCIATED VECTORS AND DEGENERATE
DISTRIBUTION SEMIGROUPS 143 2.2.2 WELL-POSEDNESS IN THE SENSE OF
DISTRIBUTIONS 149 2.2.3 WELL-POSEDNESS IN THE SPACE OF EXPONENTIAL
DISTRIBUTIONS 160 2.3 ULTRADISTRIBUTIONS AND NEW DISTRIBUTIONS 161 2.3.1
ABSTRACT ULTRADISTRIBUTIONS 162 2.3.2 THE CAUCHY PROBLEM IN SPACES OF
ABSTRACT ULTRADISTRIBUTIONS 165 2.3.3 THE CAUCHY PROBLEM IN SPACES OF
NEW DISTRIBUTIONS 173 3 REGULARIZATION METHODS 179 3.1 THE ILL-POSED
CAUCHY PROBLEM 179 3.1.1 QUASI-REVERSIBILITY METHOD 179 3.1.2 AUXILIARY
BOUNDED CONDITIONS (ABC) METHOD . . . . 185 3.1.3 CARASSO S METHOD : . .
188 3.2 REGULARIZATION AND REGULARIZED SEMIGROUPS 190 3.2.1 COMPARISON
OF THE ABC AND THE QUASI-REVERSIBILITY METHODS 190 3.2.2 DIFFERENTIAL
AND VARIATIONAL METHODS OF REGULARIZATION 194 IX 3.2.3 REGULARIZING
OPERATORS AND LOCAL C-REGULARIZED SEMI- GROUPS 196 3.2.4 REGULARIZATION
OF SLIGHTLY ILL-POSED PROBLEMS . . . . 199 BIBLIOGRAPHIC REMARK 203
BIBLIOGRAPHY 205 GLOSSARY OF NOTATION 229 INDEX 233
|
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| dewey-tens | 510 - Mathematics |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:57:43Z |
| institution | BVB |
| isbn | 1584882506 |
| language | English |
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| physical | XXI, 236 S. |
| publishDate | 2001 |
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| publisher | Chapman & Hall/CRC |
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| series | Chapman & Hall CRC monographs and surveys in pure and applied mathematics |
| series2 | Chapman & Hall CRC monographs and surveys in pure and applied mathematics |
| spelling | Melnikova, Irina V. Verfasser aut Abstract Cauchy problems three approaches Irina V. Melnikova ; Alexei Filinkov Boca Raton [u.a.] Chapman & Hall/CRC 2001 XXI, 236 S. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall CRC monographs and surveys in pure and applied mathematics 120 Cauchy, Problème de Cauchy problem Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd rswk-swf Cauchy-Anfangswertproblem (DE-588)4147404-1 s DE-604 Filinkov, Alexei Verfasser aut Chapman & Hall CRC monographs and surveys in pure and applied mathematics 120 (DE-604)BV013350872 120 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009662711&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Melnikova, Irina V. Filinkov, Alexei Abstract Cauchy problems three approaches Chapman & Hall CRC monographs and surveys in pure and applied mathematics Cauchy, Problème de Cauchy problem Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd |
| subject_GND | (DE-588)4147404-1 |
| title | Abstract Cauchy problems three approaches |
| title_auth | Abstract Cauchy problems three approaches |
| title_exact_search | Abstract Cauchy problems three approaches |
| title_full | Abstract Cauchy problems three approaches Irina V. Melnikova ; Alexei Filinkov |
| title_fullStr | Abstract Cauchy problems three approaches Irina V. Melnikova ; Alexei Filinkov |
| title_full_unstemmed | Abstract Cauchy problems three approaches Irina V. Melnikova ; Alexei Filinkov |
| title_short | Abstract Cauchy problems |
| title_sort | abstract cauchy problems three approaches |
| title_sub | three approaches |
| topic | Cauchy, Problème de Cauchy problem Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd |
| topic_facet | Cauchy, Problème de Cauchy problem Cauchy-Anfangswertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009662711&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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