A concise guide to semigroups and evolution equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1994
|
| Series: | Series on advances in mathematics for applied sciences
19 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 164 S. |
| ISBN: | 9810212941 |
Staff View
MARC
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| 100 | 1 | |a Belleni-Morante, Aldo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A concise guide to semigroups and evolution equations |c Aldo Belleni-Morante |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1994 | |
| 300 | |a XII, 164 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Series on advances in mathematics for applied sciences |v 19 | |
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| 650 | 7 | |a Semigroupes |2 ram | |
| 650 | 4 | |a Evolution equations | |
| 650 | 4 | |a Semigroups | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE vii
1. TWO TYPICAL EVOLUTION PROBLEMS 1
1.1. A linear problem 1
Note 1.1 Strong continuity 6
Note 1.2. Generalized derivatives 7
1.2. A semilinear problem 8
Note 1.3. Subspaces of a Baiiach space 12
2. SEMIGROUPS GENERATED BY BOUNDED OPERATORS 14
2.1. Time independent bounded operators 14
Note 2.1. Convergence of a sequence of operators 21
Note 2.2. Some technicalities 23
Note 2.3. Two different strong derivatives 24
Note 2.4. Gronwall s lemma 25
2.2. Time dependent bounded operators 26
rx
X A Concise Guide to Semigroups
3. SEMIGROUPS GENERATED BY A e 7(l,0pV) 35
3.1. Introduction 35
3.2. The evolution problem (41) 43
Note 3.1. Dense subset 50
Note 3.2. Closed operators 51
Note 3.3. d(a2) as a dense subset of X 52
Note 3.4. The vector space C^ 53
Note 3.5. Hilbert spaces 53
4. THE CASES A e G(M,P ;X) AND A e G ( fi,X) 55
4.1. Thecase A eG(M,fi,x) 55
4.2. The case A g{ ,P;X) 57
Note 4.1. Holder inequality 59
4.3. The abstract evolution problem with A e G(m ,J3; x) 60
4.4. Positive solutions 61
Note 4.2. Positivity of the strong Riemann integral 65
4.5. Thecase A e G (l,0,x) 65
5. BOUNDED PERTURBATIONS 69
5.1. Introduction 69
5.2. Bounded perturbations 70
Note 5.1. Norm of the product of two bounded operators 73
Note 5.2. The operator (/i / Bo) with Bo eS(X) 73
5.3. The integral version of system (78) 74
Note 5.3. Bounded operators defined on the same dense set 78
6. HOLOMORPHIC SEMIGROUPS 79
6.1. Introduction 79
6.2. The semigroup generated by A e %{a, A/,0, X) 81
Contents v.
Note 6.1. Line integrals 86
6.3. Further properties of T(t) 87
6.4. The homogeneous and the nonhomogeneous evolution problems 93
7. A LINEAR EVOLUTION PROBLEM 96
7.1. Introduction 96
7.2. The operators T, B and K 97
7.3. Solution of the abstract problem (105) 100
8. SEMILINEAR EVOLUTION PROBLEMS 106
8.1. Introduction 106
Note 8.1. Lipschitz operators 110
8.2. The nonlinear integral equation (120) 111
Note 8.2. Convex sets 115
Note 8.3. Frechet derivative 116
Note 8.4. Contraction mapping theorem 118
8.3. Strict and mild solutions of system (115) 118
Note 8.5. Some technicalities 127
Note 8.6. Bounded convergence theorem 129
Note 8.7. Some properties of A, eG{M,/]; X) 129
8.4. Global in time solutions of (115) 130
8.5. A semilinear problem from populationn theory:
solution local in time 131
8.6. A semilinear problem from population theory:
positivity properties 136
8.7. A semilinear problem from population theory:
solution global in time, part I 140
8.8. A semilinear problem from population theory:
solution global in time, part II 142
XII A Concise Guide to Semigroups
8.9. Some remarks on the nonhomogeneous case 146
APPENDIX A: Lebesgue measure and Lebesgue integral 149
APPENDIX B: Banach spaces 153
REFERENCES 158
SUBJECT INDEX 161
|
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV012738953 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:32:50Z |
| institution | BVB |
| isbn | 9810212941 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008662317 |
| oclc_num | 30032379 |
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| physical | XII, 164 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on advances in mathematics for applied sciences |
| series2 | Series on advances in mathematics for applied sciences |
| spelling | Belleni-Morante, Aldo Verfasser aut A concise guide to semigroups and evolution equations Aldo Belleni-Morante Singapore [u.a.] World Scientific 1994 XII, 164 S. txt rdacontent n rdamedia nc rdacarrier Series on advances in mathematics for applied sciences 19 Equation évolution Semigroupes ram Evolution equations Semigroups Halbgruppe (DE-588)4022990-7 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Halbgruppe (DE-588)4022990-7 s Evolutionsgleichung (DE-588)4129061-6 s DE-604 Series on advances in mathematics for applied sciences 19 (DE-604)BV004569239 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008662317&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Belleni-Morante, Aldo A concise guide to semigroups and evolution equations Series on advances in mathematics for applied sciences Equation évolution Semigroupes ram Evolution equations Semigroups Halbgruppe (DE-588)4022990-7 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4022990-7 (DE-588)4129061-6 |
| title | A concise guide to semigroups and evolution equations |
| title_auth | A concise guide to semigroups and evolution equations |
| title_exact_search | A concise guide to semigroups and evolution equations |
| title_full | A concise guide to semigroups and evolution equations Aldo Belleni-Morante |
| title_fullStr | A concise guide to semigroups and evolution equations Aldo Belleni-Morante |
| title_full_unstemmed | A concise guide to semigroups and evolution equations Aldo Belleni-Morante |
| title_short | A concise guide to semigroups and evolution equations |
| title_sort | a concise guide to semigroups and evolution equations |
| topic | Equation évolution Semigroupes ram Evolution equations Semigroups Halbgruppe (DE-588)4022990-7 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Equation évolution Semigroupes Evolution equations Semigroups Halbgruppe Evolutionsgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008662317&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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