An introduction to semilinear evolution equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
Oxford
Clarendon Press
1998
|
| Ausgabe: | Rev. ed. |
| Schriftenreihe: | Oxford lecture series in mathematics and its applications
13 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIV, 186 S. |
| ISBN: | 019850277X |
Internformat
MARC
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| 100 | 1 | |a Cazenave, Thierry |d 1954- |e Verfasser |0 (DE-588)130600016 |4 aut | |
| 240 | 1 | 0 | |a Introduction aux problémes d'évolution semi-linéaires |
| 245 | 1 | 0 | |a An introduction to semilinear evolution equations |c Thierry Cazenave and Alain Haraux |
| 250 | |a Rev. ed. | ||
| 264 | 1 | |a Oxford |b Clarendon Press |c 1998 | |
| 300 | |a XIV, 186 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford lecture series in mathematics and its applications |v 13 | |
| 490 | 0 | |a Oxford science publications | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Equation Klein-Gordon |2 ram | |
| 650 | 7 | |a Equation Schrödinger |2 jussieu | |
| 650 | 7 | |a Equation évolution semi-linéaire |2 ram | |
| 650 | 7 | |a Opérateur dissipatif |2 jusssieu | |
| 650 | 7 | |a Stabilité solution stationnaire |2 jussieu | |
| 650 | 7 | |a Théorème Hille-Yosida-Phillips |2 jussieu | |
| 650 | 7 | |a Équation de la chaleur |2 ram | |
| 650 | 7 | |a Équations d'évolution - Théorie asymptotique |2 ram | |
| 650 | 7 | |a Équations d'évolution |2 ram | |
| 650 | 4 | |a Evolution equations | |
| 650 | 4 | |a Evolution equations |x Asymptotic theory | |
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Datensatz im Suchindex
| _version_ | 1804126606885650432 |
|---|---|
| adam_text | Contents
Notation xiii
1. Preliminary results 1
1.1. Some abstract tools 1
1.2. The exponential of a linear continuous operator 1
1.3. Sobolev spaces 2
1.4. Vector valued functions 4
1.4.1. Measurable functions 4
1.4.2. Integrable functions 7
1.4.3. The spaces LP(I, X) 8
1.4.4. Vector valued distributions 10
1.4.5. The spaces W^i^X) 13
2. m dissipative operators 18
2.1. Unbounded operators in Banach spaces 18
2.2. Definition and main properties of m dissipative operators ... 19
2.3. Extrapolation 21
2.4. Unbounded operators in Hilbert spaces 22
2.5. Complex Hilbert spaces 25
2.6. Examples in the theory of partial differential equations .... 26
2.6:1. The Laplacian in an open subset of RN: L2 theory . . . 26
2.6.2. The Laplacian in an open subset of RN: Co theory . . . 27
2.6.3. The wave operator (or the Klein Gordon operator)
in JJg(n) x L2(Sl) 29
2.6.4. The wave operator (or the Klein Gordon operator)
in L2(fi) x iT J(fi) 30
2.6.5. The Schrodinger operator 31
3. The Hille Yosida Phillips Theorem and applications .... 33
3.1. The semigroup generated by an m dissipative operator .... 33
3.2. Two important special cases 35
3.3. Extrapolation and weak solutions 38
3.4. Contraction semigroups and their generators 39
3.5. Examples in the theory of partial differential equations .... 42
x Contents
3.5.1. The heat equation 42
3.5.2. The wave equation (or the Klein Gordon equation)... 47
3.5.3. The Schrodinger equation 47
3.5.4. The Schrodinger equation in RN 48
4. Inhomogeneous equations and abstract semilinear
problems 50
4.1. Inhomogeneous equations 50
4.2. Gronwall s lemma 54
4.3. Semilinear problems 55
4.3.1. A result of local existence 56
4.3.2. Continuous dependence on initial data 59
4.3.3. Regularity 60
4.4. Isometry groups 61
5. The heat equation 62
5.1. Preliminaries 62
5.2. Local existence 64
5.3. Global existence 65
5.4. Blow up in finite time 72
5.5. Application to a model case 76
6. The Klein Gordon equation 78
6.1. Preliminaries 78
6.1.1. An abstract result 78
6.1.2. Functional on H (n) 79
6.2. Local existence 82
6.3. Global existence 84
6.4. Blow up in finite time 87
6.5. Application to a model case 89
7. The Schrodinger equation 91
7.1. Preliminaries 91
7.2. A general result 92
7.3. The linear Schrodinger equation in RN 95
7.4. The non linear Schrodinger equation in RN: local existence . . 100
7.4.1. Some estimates 101
7.4.2. Proof of Theorem 7.4.1 106
7.5. The non linear Schrodinger equation in RN: global existence . . 112
Contents xi
7.6. The non linear Schrodinger equation in RN: blow up
in finite time 114
7.7. A remark concerning behaviour at infinity 120
7.8. Application to a model case 121
8. Bounds on global solutions 124
8.1. The heat equation 124
8.1.1. A singular Gronwall s lemma: application to the heat
equation 125
8.1.2. Uniform estimates 129
8.2. The Klein Gordon equation 130
8.3. The non autonomous heat equation 134
8.3.1. The Cauchy problem for the non autonomous heat
equation 134
8.3.2. A priori estimates 135
8.4. The dissipative non autonomous Klein Gordon equation . . . 137
9. The invariance principle and some applications 142
9.1. Abstract dynamical systems 142
9.2. Liapunov functions and the invariance principle 143
9.3. A dynamical system associated with a semilinear evolution
equation 145
9.4. Application to the non linear heat equation 146
9.5. Application to a dissipative Klein Gordon equation 149
10. Stability of stationary solutions 154
10.1. Definitions and simple examples 154
10.2. A simple general result 156
10.3. Exponentially stable systems governed by PDE 158
10.4. Stability and positivity 164
10.4.1. The one dimensional case 165
10.4.2. The multidimensional case 167
Bibliography 169
Index 185
|
| any_adam_object | 1 |
| author | Cazenave, Thierry 1954- Haraux, Alain |
| author_GND | (DE-588)130600016 |
| author_facet | Cazenave, Thierry 1954- Haraux, Alain |
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| author_sort | Cazenave, Thierry 1954- |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)40542301 (DE-599)BVBBV012010418 |
| 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 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Rev. ed. |
| format | Book |
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| id | DE-604.BV012010418 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:20:08Z |
| institution | BVB |
| isbn | 019850277X |
| language | English French |
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| physical | XIV, 186 S. |
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| publisher | Clarendon Press |
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| series | Oxford lecture series in mathematics and its applications |
| series2 | Oxford lecture series in mathematics and its applications Oxford science publications |
| spelling | Cazenave, Thierry 1954- Verfasser (DE-588)130600016 aut Introduction aux problémes d'évolution semi-linéaires An introduction to semilinear evolution equations Thierry Cazenave and Alain Haraux Rev. ed. Oxford Clarendon Press 1998 XIV, 186 S. txt rdacontent n rdamedia nc rdacarrier Oxford lecture series in mathematics and its applications 13 Oxford science publications Hier auch später erschienene, unveränderte Nachdrucke Equation Klein-Gordon ram Equation Schrödinger jussieu Equation évolution semi-linéaire ram Opérateur dissipatif jusssieu Stabilité solution stationnaire jussieu Théorème Hille-Yosida-Phillips jussieu Équation de la chaleur ram Équations d'évolution - Théorie asymptotique ram Équations d'évolution ram Evolution equations Evolution equations Asymptotic theory Semilineare Differentialgleichung (DE-588)4180958-0 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Semilineare Operatorgleichung (DE-588)4180961-0 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 s DE-604 Semilineare Operatorgleichung (DE-588)4180961-0 s Semilineare Differentialgleichung (DE-588)4180958-0 s Haraux, Alain Verfasser aut Oxford lecture series in mathematics and its applications 13 (DE-604)BV009910017 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008127991&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cazenave, Thierry 1954- Haraux, Alain An introduction to semilinear evolution equations Oxford lecture series in mathematics and its applications Equation Klein-Gordon ram Equation Schrödinger jussieu Equation évolution semi-linéaire ram Opérateur dissipatif jusssieu Stabilité solution stationnaire jussieu Théorème Hille-Yosida-Phillips jussieu Équation de la chaleur ram Équations d'évolution - Théorie asymptotique ram Équations d'évolution ram Evolution equations Evolution equations Asymptotic theory Semilineare Differentialgleichung (DE-588)4180958-0 gnd Evolutionsgleichung (DE-588)4129061-6 gnd Semilineare Operatorgleichung (DE-588)4180961-0 gnd |
| subject_GND | (DE-588)4180958-0 (DE-588)4129061-6 (DE-588)4180961-0 |
| title | An introduction to semilinear evolution equations |
| title_alt | Introduction aux problémes d'évolution semi-linéaires |
| title_auth | An introduction to semilinear evolution equations |
| title_exact_search | An introduction to semilinear evolution equations |
| title_full | An introduction to semilinear evolution equations Thierry Cazenave and Alain Haraux |
| title_fullStr | An introduction to semilinear evolution equations Thierry Cazenave and Alain Haraux |
| title_full_unstemmed | An introduction to semilinear evolution equations Thierry Cazenave and Alain Haraux |
| title_short | An introduction to semilinear evolution equations |
| title_sort | an introduction to semilinear evolution equations |
| topic | Equation Klein-Gordon ram Equation Schrödinger jussieu Equation évolution semi-linéaire ram Opérateur dissipatif jusssieu Stabilité solution stationnaire jussieu Théorème Hille-Yosida-Phillips jussieu Équation de la chaleur ram Équations d'évolution - Théorie asymptotique ram Équations d'évolution ram Evolution equations Evolution equations Asymptotic theory Semilineare Differentialgleichung (DE-588)4180958-0 gnd Evolutionsgleichung (DE-588)4129061-6 gnd Semilineare Operatorgleichung (DE-588)4180961-0 gnd |
| topic_facet | Equation Klein-Gordon Equation Schrödinger Equation évolution semi-linéaire Opérateur dissipatif Stabilité solution stationnaire Théorème Hille-Yosida-Phillips Équation de la chaleur Équations d'évolution - Théorie asymptotique Équations d'évolution Evolution equations Evolution equations Asymptotic theory Semilineare Differentialgleichung Evolutionsgleichung Semilineare Operatorgleichung |
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