Holdings: Abstract Cauchy problems

Abstract Cauchy problems: three approaches

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Bibliographic Details
Main Authors:	Melnikova, Irina V. (Author), Filinkov, Alexei (Author)
Format:	Book
Language:	English
Published:	Boca Raton [u.a.] Chapman & Hall/CRC 2001
Series:	Chapman & Hall CRC monographs and surveys in pure and applied mathematics 120
Subjects:	Cauchy, Problème de Cauchy problem Cauchy-Anfangswertproblem
Online Access:	Inhaltsverzeichnis
Physical Description:	XXI, 236 S.
ISBN:	1584882506

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MARC


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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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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
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