Blow-up theories for semilinear parabolic equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Lecture notes in mathematics
2018 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | X, 127 S. 235 mm x 155 mm |
| ISBN: | 3642184596 9783642184598 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV037336059 | ||
| 003 | DE-604 | ||
| 005 | 20110617 | ||
| 007 | t | ||
| 008 | 110413s2011 gw |||| 00||| eng d | ||
| 016 | 7 | |a 1009310666 |2 DE-101 | |
| 020 | |a 3642184596 |c Pb. : ca. EUR 37.40 (DE) (freier Pr.), ca. sfr 50.50 (freier Pr.) |9 3-642-18459-6 | ||
| 020 | |a 9783642184598 |c Pb. : ca. EUR 37.40 (DE) (freier Pr.), ca. sfr 50.50 (freier Pr.) |9 978-3-642-18459-8 | ||
| 035 | |a (OCoLC)723386572 | ||
| 035 | |a (DE-599)DNB1009310666 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-824 |a DE-91G |a DE-83 |a DE-188 |a DE-11 |a DE-19 |a DE-355 | ||
| 082 | 0 | |a 515.3534 |2 22/ger | |
| 084 | |a SI 850 |0 (DE-625)143199: |2 rvk | ||
| 084 | |a MAT 356f |2 stub | ||
| 084 | |a 35K10 |2 msc | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Hu, Bei |d 1962- |e Verfasser |0 (DE-588)123719631 |4 aut | |
| 245 | 1 | 0 | |a Blow-up theories for semilinear parabolic equations |c Bei Hu |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
| 300 | |a X, 127 S. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 2018 | |
| 650 | 0 | 7 | |a Semilineare parabolische Differentialgleichung |0 (DE-588)4180962-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Blowing up |0 (DE-588)4508027-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Semilineare parabolische Differentialgleichung |0 (DE-588)4180962-2 |D s |
| 689 | 0 | 1 | |a Blowing up |0 (DE-588)4508027-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-642-18460-4 |
| 830 | 0 | |a Lecture notes in mathematics |v 2018 |w (DE-604)BV000676446 |9 2018 | |
| 856 | 4 | 2 | |m X:MVB |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=3644407&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-022489872 | |
Record in the Search Index
| _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- |
| author_role | aut |
| author_sort | Hu, Bei 1962- |
| author_variant | b h bh |
| building | Verbundindex |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV037336059</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20110617</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">110413s2011 gw |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1009310666</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3642184596</subfield><subfield code="c">Pb. : ca. EUR 37.40 (DE) (freier Pr.), ca. sfr 50.50 (freier Pr.)</subfield><subfield code="9">3-642-18459-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642184598</subfield><subfield code="c">Pb. : ca. EUR 37.40 (DE) (freier Pr.), ca. sfr 50.50 (freier Pr.)</subfield><subfield code="9">978-3-642-18459-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)723386572</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1009310666</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-355</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.3534</subfield><subfield code="2">22/ger</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 356f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">35K10</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hu, Bei</subfield><subfield code="d">1962-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)123719631</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Blow-up theories for semilinear parabolic equations</subfield><subfield code="c">Bei Hu</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 127 S.</subfield><subfield code="c">235 mm x 155 mm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">2018</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Semilineare parabolische Differentialgleichung</subfield><subfield code="0">(DE-588)4180962-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Blowing up</subfield><subfield code="0">(DE-588)4508027-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Semilineare parabolische Differentialgleichung</subfield><subfield code="0">(DE-588)4180962-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Blowing up</subfield><subfield code="0">(DE-588)4508027-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-642-18460-4</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">2018</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">2018</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">X:MVB</subfield><subfield code="q">text/html</subfield><subfield code="u">http://deposit.dnb.de/cgi-bin/dokserv?id=3644407&prov=M&dok_var=1&dok_ext=htm</subfield><subfield code="3">Inhaltstext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-022489872</subfield></datafield></record></collection> |
| 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 | |
| owner | DE-824 DE-91G DE-BY-TUM DE-83 DE-188 DE-11 DE-19 DE-BY-UBM DE-355 DE-BY-UBR |
| owner_facet | DE-824 DE-91G DE-BY-TUM DE-83 DE-188 DE-11 DE-19 DE-BY-UBM DE-355 DE-BY-UBR |
| 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 |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3644407&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=022489872&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT hubei blowuptheoriesforsemilinearparabolicequations |