A unified theory of nonlinear operator and evolution equations with applications: a new approach to nonlinear partial differential equations
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Dekker
1986
|
| Series: | Monographs and textbooks in pure and applied mathematics
103 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 292 S. |
| ISBN: | 0824776135 |
Staff View
MARC
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| 100 | 1 | |a Altman, Mieczyslaw |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A unified theory of nonlinear operator and evolution equations with applications |b a new approach to nonlinear partial differential equations |
| 264 | 1 | |a New York u.a. |b Dekker |c 1986 | |
| 300 | |a XIV, 292 S. | ||
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| 650 | 4 | |a Operator equations, Nonlinear | |
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Record in the Search Index
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| adam_text | Contents
PREFACE v
Chapter 1 CONVEX APPROXIMATE LINEARIZATION AND
GLOBAL LINEARIZATION ITERATIVE METHODS 1
1. An iterative method of contractor
directions, GLIM I 1
2. An iterative method with stepsize 1,
GLIM II 9
3. A rapidly convergent iteration method,
GLIM III 14
Chapter 2 SMOOTHING OPERATORS COMBINED WITH ELLIPTIC
REGULARIZATION AND THE DEGREE OF ELLIPTIC
REGULARIZATION 24
1. GLIM I in a scale of Banach spaces 25
2. GLIM 11 in a scale of Banach spaces 39
3. GLIM III in a scale of Banach spaces 46
Chapter 3 NONLINEAR EQUATIONS IN A SCALE OF HILBERT
SOBOLEV SPACES, I 55
1. A special case of elliptic regularizatlon
of degree k = 1/2 56
2. Nonlinear partial differential equations 64
3. Systems of nonlinear partial differential
equations 66
4. Periodic solutions of nonlinear hyperbolic
partial differential equations 70
5. Linear equations with small nonlinear
perturbations 74
xi
xii Contents
Chapter 4 NONLINEAR EQUATIONS IN A SCALE OF HILBERT
SOBOLEV SPACES, II 77
1. A nonlinear existence theorem 78
2. Nonlinear systems of first order partial
differential equations 88
Chapter 5 NONLINEAR EQUATIONS IN A SCALE OF HILBERT
SOBOLEV SPACES, III 92
1. A nonlinear existence theorem 92
2. Nonlinear systems of partial differential
equations 99
Chapter 6 ELLIPTIC REGULARIZATION WITHOUT SMOOTHING
OPERATORS 102
1. Elliptic regularization and GLIM I 102
2. Elliptic regularization and GLIM II 105
3. Elliptic regularization and GLIM III 108
Chapter 7 CONVEX APPROXIMATE LINEARIZATION AND GLOBAL
LINEARIZATION ITERATIVE METHODS FOR NONLINEAR
EVOLUTION EQUATIONS 112
1. A general existence theorem via GLIM I 114
2. A general existence theorem via GLIM II 123
3. A general existence theorem via GLIM III 129
4. An application of the theory of
C semigroups 136
Chapter 8 SMOOTHING OPERATORS COMBINED WITH ELLIPTIC
REGULARIZATION AND THE DEGREE OF ELLIPTIC
REGULARIZATION FOR NONLINEAR EVOLUTION
EQUATIONS 138
1. A general existence theorem for nonlinear
evolution equations via GLIM I in a scale
of Banach spaces 138
2. A general existence theorem for nonlinear
evolution equations via GLIM II in a
scale of Banach spaces 147
3. A general existence theorem for nonlinear
evolution equations via GLIM III in a
scale of Banach spaces 155
4. Solving nonlinear evolution equations
via linearized evolution equations 165
Chapter 9 ELLIPTIC REGULARIZATION WITHOUT SMOOTHING
OPERATORS FOR NONLINEAR EVOLUTION EQUATIONS 167
1. Elliptic regularization and GLIM I for
nonlinear evolution equations 167
2. Elliptic regularization and GLIM II for
nonlinear evolution equations 170
Contents xiii
3. Elliptic regularization and GLIM III
for nonlinear evolution equations 170
Chapter 10 STRONGLY QUASILINEAR EVOLUTION EQUATIONS 175
1. Strongly quasi linear evolution equations
and convex approximate linearization 178
2. Smoothing operators combined with elliptic
regularization for strongly quasi linear
evolution equations and an iterative
method of contractor directions 190
3. Elliptic regularization without smoothing
operators 203
Chapter 11 QUASILINEAR EVOLUTION EQUATIONS 209
1. Convex linearization and a method of
contractor directions 209
2. A simplified approach to linear
evolution equations 223
3. A general existence theorem for
quasi linear evolution equations 228
4. An application of the simplified approach
to linear evolution equations to solving
quasi linear evolution equations 237
5. An existence theorem using the exact
evolution operator 239
6. An existence theorem using the approximate
evolution operator 244
Appendix 1 ITERATIVE METHODS OF CONTRACTOR DIRECTIONS 249
1. Introduction 249
2. The fundamental lemma for iterative
methods of contractor directions 250
3. Iterative methods of contractor directions 252
4. A general iterative method of contractor
directions 256
5. Convergence of the damped Newton Kantorovic
method with approximate solutions of the
linearized equations for operators with
continuous Fre chet derivatives 258
6. An iterative method of contractor direc¬
tions for nondifferentiable operators 260
7. The B property 263
Appendix 2 THE METHOD OF CONTRACTOR DIRECTIONS FOR
NONLINEAR ELLIPTIC EQUATIONS 265
1. A general existence theorem 265
2. The Agmon Douglis Nirenberg estimates 272
3. The boundary value problem for nonlinear
elliptic equations 274
xiv Contents
Appendix 3 AN APPLICATION OF THE METHOD OF CONTRACTOR
DIRECTIONS TO THE BOLTZMANN EQUATION FOR
NEUTRON TRANSPORT IN L1 SPACE 276
1. Introduction 276
2. A generalization of the Boltzmann
equation 277
REFERENCES 287
INDEX 291
|
| any_adam_object | 1 |
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| dewey-full | 515.7/248 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7/248 |
| dewey-search | 515.7/248 |
| dewey-sort | 3515.7 3248 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000686660 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:17:47Z |
| institution | BVB |
| isbn | 0824776135 |
| language | English |
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| physical | XIV, 292 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Dekker |
| record_format | marc |
| series | Monographs and textbooks in pure and applied mathematics |
| series2 | Monographs and textbooks in pure and applied mathematics |
| spelling | Altman, Mieczyslaw Verfasser aut A unified theory of nonlinear operator and evolution equations with applications a new approach to nonlinear partial differential equations New York u.a. Dekker 1986 XIV, 292 S. txt rdacontent n rdamedia nc rdacarrier Monographs and textbooks in pure and applied mathematics 103 Équations d'évolution non linéaires Équations à opérateurs non linéaires Evolution equations, Nonlinear Operator equations, Nonlinear Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd rswk-swf Nichtlineare Operatorgleichung (DE-588)4171756-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s DE-604 Nichtlineare Evolutionsgleichung (DE-588)4221363-0 s Nichtlineare Operatorgleichung (DE-588)4171756-9 s Monographs and textbooks in pure and applied mathematics 103 (DE-604)BV000001885 103 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000428229&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Altman, Mieczyslaw A unified theory of nonlinear operator and evolution equations with applications a new approach to nonlinear partial differential equations Monographs and textbooks in pure and applied mathematics Équations d'évolution non linéaires Équations à opérateurs non linéaires Evolution equations, Nonlinear Operator equations, Nonlinear Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Nichtlineare Operatorgleichung (DE-588)4171756-9 gnd |
| subject_GND | (DE-588)4128900-6 (DE-588)4221363-0 (DE-588)4171756-9 (DE-588)1071861417 |
| title | A unified theory of nonlinear operator and evolution equations with applications a new approach to nonlinear partial differential equations |
| title_auth | A unified theory of nonlinear operator and evolution equations with applications a new approach to nonlinear partial differential equations |
| title_exact_search | A unified theory of nonlinear operator and evolution equations with applications a new approach to nonlinear partial differential equations |
| title_full | A unified theory of nonlinear operator and evolution equations with applications a new approach to nonlinear partial differential equations |
| title_fullStr | A unified theory of nonlinear operator and evolution equations with applications a new approach to nonlinear partial differential equations |
| title_full_unstemmed | A unified theory of nonlinear operator and evolution equations with applications a new approach to nonlinear partial differential equations |
| title_short | A unified theory of nonlinear operator and evolution equations with applications |
| title_sort | a unified theory of nonlinear operator and evolution equations with applications a new approach to nonlinear partial differential equations |
| title_sub | a new approach to nonlinear partial differential equations |
| topic | Équations d'évolution non linéaires Équations à opérateurs non linéaires Evolution equations, Nonlinear Operator equations, Nonlinear Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Nichtlineare Operatorgleichung (DE-588)4171756-9 gnd |
| topic_facet | Équations d'évolution non linéaires Équations à opérateurs non linéaires Evolution equations, Nonlinear Operator equations, Nonlinear Nichtlineare partielle Differentialgleichung Nichtlineare Evolutionsgleichung Nichtlineare Operatorgleichung Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000428229&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
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