Blow-up theories for semilinear parabolic equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schriftenreihe: | Lecture notes in mathematics
2018 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | X, 127 S. 235 mm x 155 mm |
| ISBN: | 3642184596 9783642184598 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1805095823669723136 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
2 A REVIEW OF ELLIPTIC THEORIES 7
2.1 WEAK SOLUTIONS AND A WEAK MAXIMUM PRINCIPLE 7
2.2 SCHAUDER THEORY 8
2.3 A STRONG MAXIMUM PRINCIPLE 11
2.4 DE GIORGI-NASH-MOSER ESTIMATES 12
2.5 L P ESTIMATES 13
2.6 KRYLOV-SAFONOV ESTIMATES 15
2.7 POINCARE'S INEQUALITY AND EMBEDDING THEOREMS 16
2.8 EXERCISES 17
3 A REVIEW OF PARABOLIC THEORIES 19
3.1 WEAK SOLUTIONS AND A WEAK MAXIMUM PRINCIPLE 19
3.2 SCHAUDER THEORY 20
3.3 A STRONG MAXIMUM PRINCIPLE 22
3.4 DE GIORGI-NASH-MOSER ESTIMATES 23
3.5 L P ESTIMATES 24
3.6 KRYLOV-SAFONOV ESTIMATES 25
3.7 EMBEDDING THEOREMS 25
3.8 EXERCISES 27
4 A REVIEW OF FIXED POINT THEOREMS 29
4.1 FIXED POINT THEOREMS 29
4.2 EXERCISES 30
5 FINITE TIME BLOW-UP FOR EVOLUTION EQUATIONS 33
5.1 FINITE TIME BLOW-UP: KAPLAN'S FIRST EIGENVALUE METHOD 34 5.2 FINITE
TIME BLOW-UP: CONCAVITY METHOD 36
5.3 FINITE TIME BLOW-UP: A COMPARISON METHOD 38
5.4 FUJITA TYPES OF RESULTS ON UNBOUNDED DOMAINS 39
5.5 EXERCISES 45
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1009310666
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
6 STEADY-STATE SOLUTIONS 47
6. 1 EXISTENCE: UPPER AND LOWER SOLUTION METHODS 47
6.2 THE MOVING PLANE METHOD (GIDAS-NI-NIRENBERG) 51
6.3 THE MOVING PLANE METHOD ON UNBOUNDED DOMAINS 56 6.4 EXERCISES 62
7 BLOW-UP RATE 65
7. 1 BLOW-UP RATE LOWER BOUND FOR INTERNAL HEAT SOURCE 66 7.2 BLOW-UP
RATE LOWER BOUND: A SCALING METHOD 67
7.3 BLOW-UP RATE UPPER BOUND: FRIEDMAN-MCLEOD'S METHOD 72
7.4 BLOW-UP RATE UPPER BOUND: A SCALING METHOD 77
7.5 EXERCISES 82
8 ASYMPTOTICALLY SELF-SIMILAR BLOW-UP SOLUTIONS 85
8.1 POHOZAEV IDENTITY 86
8.2 ASYMPTOTICALLY BACKWARD SELF SIMILAR BLOW-UP SOLUTIONS 87 8.3 A
METHOD FOR STUDYING ASYMPTOTIC BEHAVIOR 92
8.4 CONSTRUCTING LYAPUNOV FUNCTIONS IN ONE SPACE DIMENSION 92 8.5
EXERCISES 95
9 ONE SPACE VARIABLE CASE 97
9. 1 STURM ZERO NUMBER 97
9.2 FINITE-POINTS BLOW-UP 99
9.3 INTERSECTION COMPARISON: AN EXAMPLE OF COMPLETE BLOW-UP 103
9.4 SOLUTIONS IN SIMILARITY VARIABLES 112
9.5 EXERCISES 117
REFERENCES 119
INDEX 127 |
| any_adam_object | 1 |
| author | Hu, Bei 1962- |
| author_GND | (DE-588)123719631 |
| author_facet | Hu, Bei 1962- |
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| bvnumber | BV037336059 |
| classification_rvk | SI 850 |
| classification_tum | MAT 356f |
| ctrlnum | (OCoLC)723386572 (DE-599)DNB1009310666 |
| dewey-full | 515.3534 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3534 |
| dewey-search | 515.3534 |
| dewey-sort | 3515.3534 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV037336059 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T11:05:25Z |
| institution | BVB |
| isbn | 3642184596 9783642184598 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022489872 |
| oclc_num | 723386572 |
| open_access_boolean | |
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| physical | X, 127 S. 235 mm x 155 mm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Hu, Bei 1962- Verfasser (DE-588)123719631 aut Blow-up theories for semilinear parabolic equations Bei Hu Berlin [u.a.] Springer 2011 X, 127 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2018 Semilineare parabolische Differentialgleichung (DE-588)4180962-2 gnd rswk-swf Blowing up (DE-588)4508027-6 gnd rswk-swf Semilineare parabolische Differentialgleichung (DE-588)4180962-2 s Blowing up (DE-588)4508027-6 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-18460-4 Lecture notes in mathematics 2018 (DE-604)BV000676446 2018 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3644407&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=022489872&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hu, Bei 1962- Blow-up theories for semilinear parabolic equations Lecture notes in mathematics Semilineare parabolische Differentialgleichung (DE-588)4180962-2 gnd Blowing up (DE-588)4508027-6 gnd |
| subject_GND | (DE-588)4180962-2 (DE-588)4508027-6 |
| title | Blow-up theories for semilinear parabolic equations |
| title_auth | Blow-up theories for semilinear parabolic equations |
| title_exact_search | Blow-up theories for semilinear parabolic equations |
| title_full | Blow-up theories for semilinear parabolic equations Bei Hu |
| title_fullStr | Blow-up theories for semilinear parabolic equations Bei Hu |
| title_full_unstemmed | Blow-up theories for semilinear parabolic equations Bei Hu |
| title_short | Blow-up theories for semilinear parabolic equations |
| title_sort | blow up theories for semilinear parabolic equations |
| topic | Semilineare parabolische Differentialgleichung (DE-588)4180962-2 gnd Blowing up (DE-588)4508027-6 gnd |
| topic_facet | Semilineare parabolische Differentialgleichung Blowing up |
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| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT hubei blowuptheoriesforsemilinearparabolicequations |