Computation and stability of patterns in hyperbolic-parabolic systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Aachen
Shaker
2010
|
| Schriftenreihe: | Berichte aus der Mathematik
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 187 S. graph. Darst. |
| ISBN: | 9783832290641 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV036626318 | ||
| 003 | DE-604 | ||
| 005 | 20100909 | ||
| 007 | t | ||
| 008 | 100820s2010 d||| m||| 00||| eng d | ||
| 015 | |a 10,N18 |2 dnb | ||
| 015 | |a 10,A30 |2 dnb | ||
| 016 | 7 | |a 1001974891 |2 DE-101 | |
| 020 | |a 9783832290641 |c kart. : EUR 48.80, EUR 48.80 (AT), sfr 97.60 (freier Pr.) |9 978-3-8322-9064-1 | ||
| 024 | 3 | |a 9783832290641 | |
| 035 | |a (OCoLC)650986073 | ||
| 035 | |a (DE-599)DNB1001974891 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-634 | ||
| 082 | 0 | |a 515.353 |2 22/ger | |
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Rottmann-Matthes, Jens |e Verfasser |0 (DE-588)141247150 |4 aut | |
| 245 | 1 | 0 | |a Computation and stability of patterns in hyperbolic-parabolic systems |c Jens Rottmann-Matthes |
| 264 | 1 | |a Aachen |b Shaker |c 2010 | |
| 300 | |a VI, 187 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Berichte aus der Mathematik | |
| 502 | |a Zugl.: Bielefeld, Univ., Diss., 2010 | ||
| 650 | 0 | 7 | |a Wanderwelle |0 (DE-588)4189075-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hyperbolisches Differentialgleichungssystem |0 (DE-588)4496581-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Parabolisches Differentialgleichungssystem |0 (DE-588)4833677-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stabilität |0 (DE-588)4056693-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Asymptotisches Lösungsverhalten |0 (DE-588)4134367-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Hyperbolisches Differentialgleichungssystem |0 (DE-588)4496581-3 |D s |
| 689 | 0 | 1 | |a Parabolisches Differentialgleichungssystem |0 (DE-588)4833677-4 |D s |
| 689 | 0 | 2 | |a Wanderwelle |0 (DE-588)4189075-9 |D s |
| 689 | 0 | 3 | |a Asymptotisches Lösungsverhalten |0 (DE-588)4134367-0 |D s |
| 689 | 0 | 4 | |a Stabilität |0 (DE-588)4056693-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 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=020546254&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020546254 | ||
Datensatz im Suchindex
| _version_ | 1804143238243680256 |
|---|---|
| adam_text | CONTENTS 1 INTRODUCTION 1 2 SYMMETRIES IN PARTIAL DIFFERENTIAL EQUATIONS
9 2.1 EQUIVARIANT EVOLUTION EQUATIONS 9 2.2 EVOLUTION WITH GROUP-MOTION
12 2.3 THE METHOD OF FREEZING 15 2.3.1 FIXED PHASE CONDITION 15 2.3.2
ORTHOGONALITY PHASE CONDITION 16 2.4 RELATIVE EQUILIBRIA AND STABILITY
17 3 STABILITY FOR HYPERBOLIC SYSTEMS 19 3.1 LOCAL EXISTENCE AND
UNIQUENESS 21 3.2 SPLITTING OF THE SYSTEM 23 3.3 RESOLVENT ESTIMATES FOR
HYPERBOLIC PDAES 28 3.3.1 RESOLVENT ESTIMATES FOR LARGE S 29 3.3.2
RESOLVENT ESTIMATES IN COMPACT SETS 30 3.3.3 RESOLVENT ESTIMATES FOR S
SMALL 31 3.4 LINEAR STABILITY OF THE PDAE 33 3.5 NONLINEAR STABILITY OF
THE PDAE 39 3.5.1 ANALYSIS OF THE NONLINEAR TERMS 42 3.5.2 PROOF OF
PDAE-STABILITY 45 3.6 ASYMPTOTIC STABILITY WITH ASYMPTOTIC PHASE 48 3.7
STABILITY AND THE METHOD OF FREEZING 50 4 STABILITY FOR
HYPERBOLIC-PARABOLIC SYSTEMS 59 4.1 LOCAL EXISTENCE AND UNIQUENESS 60
4.1.1 ANALYSIS OF A PARABOLIC PROBLEM 65 4.1.2 ANALYSIS OF A HYPERBOLIC
PROBLEM 68 4.1.3 THE OPERATOR 5 IS A LOCAL CONTRACTION 69 4.1.4
UNIQUENESS OF THE WEAK SOLUTION 72 4.1.5 GLOBAL CONTINUATION 73 4.2
EQUIVALENCE OF THE PDAE AND THE PDE FORMULATION 74 4.3 RESOLVENT
ESTIMATES FOR HYPERBOLIC-PARABOLIC PDAES 82 4.3. BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/1001974891 DIGITALISIERT DURCH VI
CONTENTS 4.4.1 WELL-POSEDNESS OF THE PDAE 93 4.4.2 PROOF OF LINEAR
STABILITY 100 4.5 NONLINEAR STABILITY OF THE PDAE 104 4.6 NONLINEAR
STABILITY WITH ASYMPTOTIC PHASE 108 4.7 ASYMPTOTIC STABILITY AND THE
METHOD OF FREEZING 110 5 APPLICATIONS AND NUMERICAL EXPERIMENTS 117 5.1
AN ALGORITHM FOR THE METHOD OF FREEZING 117 5.2 APPLICATIONS AND
NUMERICAL EXPERIMENTS 118 5.2.1 HYPERBOLIC-NAGUMO EQUATION 118 5.2.2
FITZHUGH-NAGUMO MODEL 127 5.2.3 BARKLEY S MODEL 132 5.2.4 BURGERS
EQUATION 134 A EXPONENTIAL DICHOTOMIES 147 B RESOLVENT ESTIMATES 151 C
VECTOR VALUED LAPLACE TRANSFORM 155 D ANALYSIS 157 D.I INEQUALITIES 157
D.2 APPROXIMATION AND CONVOLUTION 157 D.3 NEMYTSKII OPERATORS 161 D.4
DETAILS OF SOME ESTIMATES FROM SECTION 3.5 165 E ENERGY ESTIMATES 171
E.I HYPERBOLIC SYSTEMS 171 E.2 COUPLED HYPERBOLIC-PARABOLIC SYSTEMS 171
SYMBOLS AND ABBREVIATIONS 177 BIBLIOGRAPHY 179
|
| any_adam_object | 1 |
| author | Rottmann-Matthes, Jens |
| author_GND | (DE-588)141247150 |
| author_facet | Rottmann-Matthes, Jens |
| author_role | aut |
| author_sort | Rottmann-Matthes, Jens |
| author_variant | j r m jrm |
| building | Verbundindex |
| bvnumber | BV036626318 |
| ctrlnum | (OCoLC)650986073 (DE-599)DNB1001974891 |
| 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 | Thesis Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02166nam a2200505 c 4500</leader><controlfield tag="001">BV036626318</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20100909 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">100820s2010 d||| m||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">10,N18</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">10,A30</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1001974891</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783832290641</subfield><subfield code="c">kart. : EUR 48.80, EUR 48.80 (AT), sfr 97.60 (freier Pr.)</subfield><subfield code="9">978-3-8322-9064-1</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9783832290641</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)650986073</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1001974891</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="049" ind1=" " ind2=" "><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.353</subfield><subfield code="2">22/ger</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">Rottmann-Matthes, Jens</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)141247150</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Computation and stability of patterns in hyperbolic-parabolic systems</subfield><subfield code="c">Jens Rottmann-Matthes</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Aachen</subfield><subfield code="b">Shaker</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VI, 187 S.</subfield><subfield code="b">graph. Darst.</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="0" ind2=" "><subfield code="a">Berichte aus der Mathematik</subfield></datafield><datafield tag="502" ind1=" " ind2=" "><subfield code="a">Zugl.: Bielefeld, Univ., Diss., 2010</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Wanderwelle</subfield><subfield code="0">(DE-588)4189075-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hyperbolisches Differentialgleichungssystem</subfield><subfield code="0">(DE-588)4496581-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Parabolisches Differentialgleichungssystem</subfield><subfield code="0">(DE-588)4833677-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stabilität</subfield><subfield code="0">(DE-588)4056693-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Asymptotisches Lösungsverhalten</subfield><subfield code="0">(DE-588)4134367-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4113937-9</subfield><subfield code="a">Hochschulschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Hyperbolisches Differentialgleichungssystem</subfield><subfield code="0">(DE-588)4496581-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Parabolisches Differentialgleichungssystem</subfield><subfield code="0">(DE-588)4833677-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Wanderwelle</subfield><subfield code="0">(DE-588)4189075-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Asymptotisches Lösungsverhalten</subfield><subfield code="0">(DE-588)4134367-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="4"><subfield code="a">Stabilität</subfield><subfield code="0">(DE-588)4056693-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</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=020546254&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-020546254</subfield></datafield></record></collection> |
| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV036626318 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:44:29Z |
| institution | BVB |
| isbn | 9783832290641 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020546254 |
| oclc_num | 650986073 |
| open_access_boolean | |
| owner | DE-634 |
| owner_facet | DE-634 |
| physical | VI, 187 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Shaker |
| record_format | marc |
| series2 | Berichte aus der Mathematik |
| spelling | Rottmann-Matthes, Jens Verfasser (DE-588)141247150 aut Computation and stability of patterns in hyperbolic-parabolic systems Jens Rottmann-Matthes Aachen Shaker 2010 VI, 187 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Berichte aus der Mathematik Zugl.: Bielefeld, Univ., Diss., 2010 Wanderwelle (DE-588)4189075-9 gnd rswk-swf Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd rswk-swf Parabolisches Differentialgleichungssystem (DE-588)4833677-4 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 s Parabolisches Differentialgleichungssystem (DE-588)4833677-4 s Wanderwelle (DE-588)4189075-9 s Asymptotisches Lösungsverhalten (DE-588)4134367-0 s Stabilität (DE-588)4056693-6 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020546254&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rottmann-Matthes, Jens Computation and stability of patterns in hyperbolic-parabolic systems Wanderwelle (DE-588)4189075-9 gnd Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd Parabolisches Differentialgleichungssystem (DE-588)4833677-4 gnd Stabilität (DE-588)4056693-6 gnd Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd |
| subject_GND | (DE-588)4189075-9 (DE-588)4496581-3 (DE-588)4833677-4 (DE-588)4056693-6 (DE-588)4134367-0 (DE-588)4113937-9 |
| title | Computation and stability of patterns in hyperbolic-parabolic systems |
| title_auth | Computation and stability of patterns in hyperbolic-parabolic systems |
| title_exact_search | Computation and stability of patterns in hyperbolic-parabolic systems |
| title_full | Computation and stability of patterns in hyperbolic-parabolic systems Jens Rottmann-Matthes |
| title_fullStr | Computation and stability of patterns in hyperbolic-parabolic systems Jens Rottmann-Matthes |
| title_full_unstemmed | Computation and stability of patterns in hyperbolic-parabolic systems Jens Rottmann-Matthes |
| title_short | Computation and stability of patterns in hyperbolic-parabolic systems |
| title_sort | computation and stability of patterns in hyperbolic parabolic systems |
| topic | Wanderwelle (DE-588)4189075-9 gnd Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd Parabolisches Differentialgleichungssystem (DE-588)4833677-4 gnd Stabilität (DE-588)4056693-6 gnd Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd |
| topic_facet | Wanderwelle Hyperbolisches Differentialgleichungssystem Parabolisches Differentialgleichungssystem Stabilität Asymptotisches Lösungsverhalten Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020546254&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rottmannmatthesjens computationandstabilityofpatternsinhyperbolicparabolicsystems |