Nonlinear evolution operators and semigroups: applications to partial differential equations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1987
|
| Schriftenreihe: | Lecture notes in mathematics
1260 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 285 S. |
| ISBN: | 3540179747 0387179747 |
Internformat
MARC
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| 100 | 1 | |a Pavel, Nicolae H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonlinear evolution operators and semigroups |b applications to partial differential equations |c Nicolae H. Pavel |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1987 | |
| 300 | |a VI, 285 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1260 | |
| 650 | 7 | |a Analyse fonctionnelle |2 ram | |
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| 650 | 4 | |a Semi-groupes | |
| 650 | 7 | |a Semigroupes |2 ram | |
| 650 | 7 | |a Théories non linéaires |2 ram | |
| 650 | 4 | |a demi-groupe | |
| 650 | 4 | |a demi-groupe non linéaire | |
| 650 | 4 | |a opérateur non linéaire | |
| 650 | 4 | |a Équations d'évolution non linéaires | |
| 650 | 4 | |a Équations différentielles | |
| 650 | 7 | |a Équations différentielles |2 ram | |
| 650 | 4 | |a équation évolution | |
| 650 | 4 | |a évolution | |
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Evolution equations, Nonlinear | |
| 650 | 4 | |a Nonlinear operators | |
| 650 | 4 | |a Semigroups | |
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| 650 | 0 | 7 | |a Halbgruppe |0 (DE-588)4022990-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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CONTENTS
Preface
Chapter 1. NONLINEAR EVOLUTION OPERATORS
§1. Preliminaries. Discrete Schemes (DS) 1
§2. The convergence of DS approximate solutions 4
2.1. The time dependence of A(t) 4
2.2. A remarkable estimate 7
§3. Convergence of DS approximate solutions and generation of Evolution Operators.
Integral solutions 14
3.1. Convergence of DS approximate solutions 14
3.2. Integral solutions 17
3.3. Evolution Operator 23
3.4. Generation of evolution operator 28
3.5. Existence of DS approximate solutions 29
3.6. The case A(t) m dissipative 32
3.7. Evolution operator and strong solutions 34
§4. Other properties of evolution operators 36
4.1. The estimate of the difference of two integral solutions 36
4.2. The relationship between U(s + h, s) and S(h)x 39
4.3. The quasi autonomous case 41
§5. Compact evolution operators 43
5.1. Necessary conditions for compactness 43
5.2. The extension of Brezis' theorem 46
§6. Other types of t dependence of A(t): conditions of Kato, Crandall Pazy 49
§7. Range condition. Tangential condition 56
Chapter 2. NONLINEAR SEMIGROUPS
§1. Discrete schemes in autonomous case 61
§2. DS limit solutions. Integral solutions Generation of nonlinear semigroups 64
§3. Other properties of nonlinear semigroups 68
3.1. Lipschitz continuity 68
3.2. The relationship of the semigroup 5x(t) and (/ tAy1. The exponential
formula of Crandall Liggett 70
§4. A generalized domain for semigroup generators 74
§5. Strong solutions 79
5.1. A characterization of strong solution under "Range conditions" 79
5.2. Strong solutions on closed subsets in continuous case. Flow invariance 82
§6. Generation of compact semigroups 88
6.1. Nonlinear compact semigroups 88
6.2. Linear compact semigroups. Hille Yosida Theorem 93
§7. Differential inclusions in Hilbert spaces.
Smoothing effect of semigroups generated by Subdifferentials 103
§8. Some results of nonlinear perturbation theory 113
8.1. Perturbation of m dissipativity 113
8.2. On the equation y € dx Ax Bx 116
8.3. Perturbation of maximal monotonicity 118
8.4. Continuous perturbation of compact semigroups generators. The case of
subgradients 120
§9. Some results on the asymptotic behaviour of nonlinear semigroups 122
VI
§10. Integral and strong solutions and smoothing effect in quasi autonomous case 129
10.1. The general case u' € Au + / 129
10.2. The case A = dj 134
10.3. Solutions everywhere differentiable at the right 137
10.4. Some results on the asymptotic behaviour of solutions 142
§11. The correspondence A + Sa(*) ¦ The existence of accretive sets 148
Chapter 3. APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS
§1. A class of (nonlinear) evolution equations associated with time dependent
domain multivalued operates 152
1.1. A general existence theory 152
1.2. The simplest proof of Peano's existence theorem 156
1.3. The behaviour of maximal (integral) solution as 11 tmax 156
§2. A class of partial differential equations with time dependent domain, modelling
long water waves of small amplitude. Evolution operators approach 159
2.1. Model equations for long waves in nonlinear dispersive systems 159
2.2. Weak solutions and classical solutions 167
§3. The semigroup approach to some partial differential equations in L1 177
3.1. Phenomena that lead to Porous Medium Equation (PME) 177
3.1.1. Thermal conduction in ionized gases at height temperature 177
3.1.2. The flow of a gas in porous media 179
3.1.3. PME as a mathematical model for population dynamic 179
3.2. Some results on PME 182
§4. Other examples of m dissipative operators and compact semigroups 188
§5. Partial differential Equations of Parabolic Type 202
5.1. The heat equation 202
5.2. Some nonlinear parabolic equations 208
5.3. A class of semilinear parabolic equations 213
§6. Wave Equation. Schrodinger Equation 227
6.1. Wave equation 227
6.2. The semilinear wave equations 229
6.3. Semilinear Schrodinger Equation 231
APPENDIX
§1. Duality mapping. Subdifferentials 234
§2. Dissipative Operators 246
§3. The regularization of a function 260
NOTES AND REFERENCES 266
REFERENCES 269
INDEX 284 |
| any_adam_object | 1 |
| author | Pavel, Nicolae H. |
| author_facet | Pavel, Nicolae H. |
| author_role | aut |
| author_sort | Pavel, Nicolae H. |
| author_variant | n h p nh nhp |
| building | Verbundindex |
| bvnumber | BV000692998 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| classification_tum | MAT 206f MAT 474f MAT 350f |
| ctrlnum | (OCoLC)230854852 (DE-599)BVBBV000692998 |
| dewey-full | 515.3/5 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 510 - Mathematics |
| dewey-raw | 515.3/5 510 |
| dewey-search | 515.3/5 510 |
| dewey-sort | 3515.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-20T04:38:30Z |
| institution | BVB |
| isbn | 3540179747 0387179747 |
| language | English |
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| physical | VI, 285 S. |
| publishDate | 1987 |
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| spelling | Pavel, Nicolae H. Verfasser aut Nonlinear evolution operators and semigroups applications to partial differential equations Nicolae H. Pavel Berlin [u.a.] Springer 1987 VI, 285 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1260 Analyse fonctionnelle ram EDP Opérateurs non linéaires Semi-groupes Semigroupes ram Théories non linéaires ram demi-groupe demi-groupe non linéaire opérateur non linéaire Équations d'évolution non linéaires Équations différentielles Équations différentielles ram équation évolution évolution Differential equations Evolution equations, Nonlinear Nonlinear operators Semigroups Nichtlinearer Evolutionsoperator (DE-588)4139676-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Evolutionsoperator (DE-588)4139677-7 gnd rswk-swf Halbgruppe (DE-588)4022990-7 gnd rswk-swf Nichtlineare Halbgruppe (DE-588)4139678-9 gnd rswk-swf Nichtlinearer Evolutionsoperator (DE-588)4139676-5 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Nichtlineare Halbgruppe (DE-588)4139678-9 s Halbgruppe (DE-588)4022990-7 s Evolutionsoperator (DE-588)4139677-7 s Lecture notes in mathematics 1260 (DE-604)BV000676446 1260 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000432251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pavel, Nicolae H. Nonlinear evolution operators and semigroups applications to partial differential equations Lecture notes in mathematics Analyse fonctionnelle ram EDP Opérateurs non linéaires Semi-groupes Semigroupes ram Théories non linéaires ram demi-groupe demi-groupe non linéaire opérateur non linéaire Équations d'évolution non linéaires Équations différentielles Équations différentielles ram équation évolution évolution Differential equations Evolution equations, Nonlinear Nonlinear operators Semigroups Nichtlinearer Evolutionsoperator (DE-588)4139676-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Evolutionsoperator (DE-588)4139677-7 gnd Halbgruppe (DE-588)4022990-7 gnd Nichtlineare Halbgruppe (DE-588)4139678-9 gnd |
| subject_GND | (DE-588)4139676-5 (DE-588)4044779-0 (DE-588)4139677-7 (DE-588)4022990-7 (DE-588)4139678-9 |
| title | Nonlinear evolution operators and semigroups applications to partial differential equations |
| title_auth | Nonlinear evolution operators and semigroups applications to partial differential equations |
| title_exact_search | Nonlinear evolution operators and semigroups applications to partial differential equations |
| title_full | Nonlinear evolution operators and semigroups applications to partial differential equations Nicolae H. Pavel |
| title_fullStr | Nonlinear evolution operators and semigroups applications to partial differential equations Nicolae H. Pavel |
| title_full_unstemmed | Nonlinear evolution operators and semigroups applications to partial differential equations Nicolae H. Pavel |
| title_short | Nonlinear evolution operators and semigroups |
| title_sort | nonlinear evolution operators and semigroups applications to partial differential equations |
| title_sub | applications to partial differential equations |
| topic | Analyse fonctionnelle ram EDP Opérateurs non linéaires Semi-groupes Semigroupes ram Théories non linéaires ram demi-groupe demi-groupe non linéaire opérateur non linéaire Équations d'évolution non linéaires Équations différentielles Équations différentielles ram équation évolution évolution Differential equations Evolution equations, Nonlinear Nonlinear operators Semigroups Nichtlinearer Evolutionsoperator (DE-588)4139676-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Evolutionsoperator (DE-588)4139677-7 gnd Halbgruppe (DE-588)4022990-7 gnd Nichtlineare Halbgruppe (DE-588)4139678-9 gnd |
| topic_facet | Analyse fonctionnelle EDP Opérateurs non linéaires Semi-groupes Semigroupes Théories non linéaires demi-groupe demi-groupe non linéaire opérateur non linéaire Équations d'évolution non linéaires Équations différentielles équation évolution évolution Differential equations Evolution equations, Nonlinear Nonlinear operators Semigroups Nichtlinearer Evolutionsoperator Partielle Differentialgleichung Evolutionsoperator Halbgruppe Nichtlineare Halbgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000432251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT pavelnicolaeh nonlinearevolutionoperatorsandsemigroupsapplicationstopartialdifferentialequations |