The Dirichlet problem for elliptic-hyperbolic equations of Keldysh type:
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2012
|
| Series: | Lecture notes in mathematics
2043 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | IX, 214 S. graph. Darst. 24 cm |
| ISBN: | 9783642244148 3642244149 9783642244155 |
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MARC
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| 100 | 1 | |a Otway, Thomas H. |e Verfasser |0 (DE-588)1020087315 |4 aut | |
| 245 | 1 | 0 | |a The Dirichlet problem for elliptic-hyperbolic equations of Keldysh type |c Thomas H. Otway |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2012 | |
| 300 | |a IX, 214 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 2043 | |
| 500 | |a Literaturangaben | ||
| 650 | 0 | 7 | |a Elliptisch-hyperbolische Differentialgleichung |0 (DE-588)4152030-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dirichlet-Problem |0 (DE-588)4129762-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Elliptisch-hyperbolische Differentialgleichung |0 (DE-588)4152030-0 |D s |
| 689 | 0 | 1 | |a Dirichlet-Problem |0 (DE-588)4129762-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |t The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type |
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Record in the Search Index
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| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 WHAT IS AN EQUATION OF KELDYSH TYPE? 1
1.1.1 REMARKS 2
1.2 WHY STUDY EQUATIONS OF KELDYSH TYPE? 3
1.3 OBJECTIVES AND ORGANIZATION OF THE COURSE 4
1.4 THE PROBLEM OF SMOOTHNESS 6
1.5 THE PROBLEM OF LOWER-ORDER TERMS 7
1.5.1 FIRST-ORDER TERMS 8
1.5.2 ZEROTH-ORDER TERMS 8
1.6 NOTATION AND CONVENTIONS 9
REFERENCES 9
2 MATHEMATICAL PRELIMINARIES 13
2.1 BOUNDARY VALUE PROBLEMS FOR ELLIPTIC-HYPERBOLIC EQUATIONS 13 2.2
WHAT IS THE RIGHT NUMBER OF BOUNDARY CONDITIONS? 16 2.3 WHAT DO WE MEAN
BY "WELL-POSED"? 18
2.4 TECHNICAL RESULTS FROM CLASSICAL ANALYSIS 19
2.4.1 A WEAK MAXIMUM PRINCIPLE 19
2.4.2 A WEIGHTED POINCARE INEQUALITY 21
2.4.3 AN INTEGRATION-BY-PARTS FORMULA 22
2.4.4 TWO THEOREMS FROM FUNCTIONAL ANALYSIS 24
2.4.5 DIVERGENT INTEGRALS 25
2.5 SYMMETRIC POSITIVE OPERATORS 26
2.5.1 THE FRIEDRICHS IDENTITIES 29
2.5.2 TWO SIMPLE EXAMPLES 33
2.6 INHOMOGENEOUS BOUNDARY CONDITIONS 34
2.7 CHAPTER APPENDIX: A SURVEY OF APPLICATIONS 35
2.7.1 VARIATIONAL INTERPRETATION 35
2.7.2 A PARTIAL LIST OF APPLICATIONS 37
2.7.3 REMARK 43
REFERENCES 43
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/101476422X
DIGITALISIERT DURCH
IMAGE 2
VIII CONTENTS
3 THE EQUATION OF CINQUINI-CIBRARIO 47
3.1 VERY BRIEF HISTORICAL REMARKS 47
3.2 TRANSFORMATION TO CANONICAL FORM 49
3.3 A CLOSED DIRICHLET PROBLEM WHICH IS CLASSICALLY ILL-POSED 50 3.4 A
CLOSED DIRICHLET PROBLEM FOR DISTRIBUTION SOLUTIONS 56 3.4.1
ALMOST-CORRECT BOUNDARY CONDITIONS 56
3.4.2 THE EXISTENCE OF DISTRIBUTION SOLUTIONS 58
3.5 A STRONG SOLUTION TO AN OPEN DIRICHLET-NEUMANN PROBLEM 61 3.5.1
D-STAR-SHAPED DOMAINS 61
3.5.2 ADMISSIBLE DOMAINS 63
3.5.3 AN EXAMPLE OF AN ADMISSIBLE DOMAIN 67
3.6 RELATION TO MAGNETICALLY DOMINATED PLASMAS 68
3.6.1 THE AXISYMMETRIC CASE 71
3.6.2 AN OPEN DIRICHLET PROBLEM FOR CINQUINI- CIBRARIO'S EQUATION WHICH
IS CLASSICALLY WELL-POSED 72
3.7 THE FUNDAMENTAL SOLUTION 75
3.7.1 THE EFFECT OF A FIRST-ORDER TERM 82
REFERENCES 83
4 THE COLD PLASMA MODEL 87
4.1 WHY STUDY THE COLD PLASMA MODEL? 88
4.1.1 VERY BRIEF HISTORICAL REMARKS 88
4.2 WAVES IN A COLD ANISOTROPIE PLASMA 88
4.2.1 ELECTROSTATIC WAVES 90
4.2.2 ELECTROMAGNETIC WAVES 93
4.3 A CLOSED DIRICHLET PROBLEM WHICH IS WEAKLY WELL POSED 99 4.4
SIMILARITY SOLUTIONS 112
4.4.1 REDUCTION TO AN ORDINARY DIFFERENTIAL EQUATION 113 4.4.2 COMPUTING
THE WEIGHT CLASS 114
4.5 WILL THESE METHODS WORK FOR CINQUINI-CIBRARIO'S EQUATION? 115
REFERENCES 119
5 LIGHT NEAR A CAUSTIC 121
5.1 A UNIFORM ASYMPTOTIC EXPANSION 124
5.2 THE COMPLEX EIKONAL EQUATION 125
5.3 THE HODOGRAPH MAP 129
5.4 A CLOSED DIRICHLET PROBLEM WHICH IS WEAKLY WELL-POSED 132 5.5 A
CLASS OF STRONGLY WELL-POSED BOUNDARY VALUE PROBLEMS 136 5.6 '
HODGE-BAECKLUND TRANSFORMATIONS 139
5.6.1 HODGE-BAECKLUND TRANSFORMATIONS IN FLUID DYNAMICS AND GEOMETRY 141
REFERENCES 143
6 PROJECTIVE GEOMETRY 145
6.1 EXTREMAL SURFACES IN MINKOWSKI 3-SPACE 145
IMAGE 3
CONTENTS IX
6.1.1 THE EXTENDED PROJECTIVE DISC 146
6.2 A CLOSED DIRICHLET PROBLEM WHICH IS CLASSICALLY ILL-POSED 147 6.2.1
WILL THESE METHODS WORK FOR MAGNANINI AND TALENTI'S MODEL? 149
6.3 AN OPEN DIRICHLET PROBLEM WHICH IS WEAKLY WELL-POSED 151 6.3.1 THE
EQUATIONS 151
6.3.2 THE ASSOCIATED SPACES 153
6.3.3 WEAK EXISTENCE 155
6.4 REMARKS ON SOME RELATED TOPICS 157
6.4.1 TRICOMI PROBLEMS 157
6.4.2 EQUATIONS IN N INDEPENDENT VARIABLES 158
6.4.3 VERY BRIEF HISTORICAL REMARKS 159
6.4.4 THE BUSEMANN EQUATION 160
6.4.5 METRICS OF MIXED RIEMANNAIN-LORENTZIAN SIGNATURE 161 REFERENCES
164
A SUMMARY AND ADDENDA 169
A. 1 VARIOUS NOTIONS OF SOLUTION 169
A.2 COMPARISON OF METHODS 170
A.3 THE EXISTENCE OF SOLUTIONS 172
A.3.1 DISTRIBUTION SOLUTIONS 172
A.3.2 WEAK SOLUTIONS 173
A.3.3 STRONG SOLUTIONS 175
A.3.4 CLASSICAL SOLUTIONS 177
A.4 THE NONEXISTENCE OF SOLUTIONS 178
A.5 ROUGH COMPARISON OF TRICOMI AND KELDYSH CLASSES 179 A.6 WEAK
SOLUTIONS IN ANISOTROPIE SOBOLEV SPACES (AFTER M. KHUN) 180
REFERENCES 182
B DIRECTIONS FOR FUTURE RESEARCH 185
B.I NONLINEAR EQUATIONS 196
REFERENCES 205
INDEX 213 |
| any_adam_object | 1 |
| author | Otway, Thomas H. |
| author_GND | (DE-588)1020087315 |
| author_facet | Otway, Thomas H. |
| author_role | aut |
| author_sort | Otway, Thomas H. |
| author_variant | t h o th tho |
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| bvnumber | BV039858668 |
| classification_rvk | SI 850 |
| classification_tum | MAT 354f MAT 357f MAT 355f |
| ctrlnum | (OCoLC)752068462 (DE-599)DNB101476422X |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-21T00:22:55Z |
| institution | BVB |
| isbn | 9783642244148 3642244149 9783642244155 |
| language | English |
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| physical | IX, 214 S. graph. Darst. 24 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Otway, Thomas H. Verfasser (DE-588)1020087315 aut The Dirichlet problem for elliptic-hyperbolic equations of Keldysh type Thomas H. Otway Berlin [u.a.] Springer 2012 IX, 214 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2043 Literaturangaben Elliptisch-hyperbolische Differentialgleichung (DE-588)4152030-0 gnd rswk-swf Dirichlet-Problem (DE-588)4129762-3 gnd rswk-swf Elliptisch-hyperbolische Differentialgleichung (DE-588)4152030-0 s Dirichlet-Problem (DE-588)4129762-3 s DE-604 Erscheint auch als Online-Ausgabe The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type Lecture notes in mathematics 2043 (DE-604)BV000676446 2043 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3873357&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024718272&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Otway, Thomas H. The Dirichlet problem for elliptic-hyperbolic equations of Keldysh type Lecture notes in mathematics Elliptisch-hyperbolische Differentialgleichung (DE-588)4152030-0 gnd Dirichlet-Problem (DE-588)4129762-3 gnd |
| subject_GND | (DE-588)4152030-0 (DE-588)4129762-3 |
| title | The Dirichlet problem for elliptic-hyperbolic equations of Keldysh type |
| title_auth | The Dirichlet problem for elliptic-hyperbolic equations of Keldysh type |
| title_exact_search | The Dirichlet problem for elliptic-hyperbolic equations of Keldysh type |
| title_full | The Dirichlet problem for elliptic-hyperbolic equations of Keldysh type Thomas H. Otway |
| title_fullStr | The Dirichlet problem for elliptic-hyperbolic equations of Keldysh type Thomas H. Otway |
| title_full_unstemmed | The Dirichlet problem for elliptic-hyperbolic equations of Keldysh type Thomas H. Otway |
| title_short | The Dirichlet problem for elliptic-hyperbolic equations of Keldysh type |
| title_sort | the dirichlet problem for elliptic hyperbolic equations of keldysh type |
| topic | Elliptisch-hyperbolische Differentialgleichung (DE-588)4152030-0 gnd Dirichlet-Problem (DE-588)4129762-3 gnd |
| topic_facet | Elliptisch-hyperbolische Differentialgleichung Dirichlet-Problem |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3873357&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024718272&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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