Boundary value problems in abstract kinetic theory:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel ; Boston ; Stuttgart
Birkhäuser Verlag
1987
|
| Series: | Operator theory
23 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 524 Seiten |
| ISBN: | 3764317655 0817617655 |
Staff View
MARC
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| 245 | 1 | 0 | |a Boundary value problems in abstract kinetic theory |c W. Greenberg, C. van der Mee, V. Protopopescu |
| 264 | 1 | |a Basel ; Boston ; Stuttgart |b Birkhäuser Verlag |c 1987 | |
| 300 | |a x, 524 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory |v 23 | |
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| 650 | 7 | |a Operatortheorie |2 gtt | |
| 650 | 7 | |a Randwaardeproblemen |2 gtt | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Initial value problems | |
| 650 | 4 | |a Kinetic theory of matter | |
| 650 | 0 | 7 | |a Transportprozess |0 (DE-588)4185932-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kinetische Theorie |0 (DE-588)4030669-0 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Protopopescu, Vladimir |0 (DE-588)1255158050 |4 aut | |
| 830 | 0 | |a Operator theory |v 23 |w (DE-604)BV000000970 |9 23 | |
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Record in the Search Index
| _version_ | 1804115058984222720 |
|---|---|
| adam_text | TABLE OF CONTENTS
Preface viii
Chapter I
ELEMENTS OF LINEAR KINETIC THEORY
1. Introduction 1
2. Historical development 7
3. Semigroups 14
4. Positive cones and Banach lattices 18
Chapter II
STRICTLY DISSIPATIVE KINETIC MODELS
1. Introduction and historical development 23
2. Solutions in H 30
3. Bounded collision operators 42
4. Unbounded collision operators 48
Chapter III
CONSERVATIVE KINETIC MODELS
1. Preliminary decompositions and reductions 55
2. Boundary value problems 68
3. Evaporation models 76
4. Reflective boundary conditions 79
Chapter IV
NON DISSIPATIVE AND NON SYMMETRIC KINETIC MODELS
1. Indefinite inner product spaces 85
2. Reduction to a strictly dissipative kinetic model 92
3. Existence and uniqueness theory 97
4. Nonsymmetric collision operators 101
Chapter V
KINETIC EQUATIONS ON FINITE DOMAINS
1. Slab geometry 108
2. Boundary value problems for nonmultiplying slab media 109
3. Boundary value problems for multiplying slab media 119
4. Reflection and transmission operators 125
5. Slabs with reflective boundary conditions 131
vi
Chapter VI
EQUIVALENCE OF DIFFERENTIAL AND INTEGRAL FORMULATIONS
1. Kinetic equations in integral form 138
2. Preliminaries on convolution operators 140
3. Equivalence theorems 144
4. Reduction of dimensionality 152
5. Reflecting boundaries 154
6. Generalizations 157
Chapter VII
SEMIGROUP FACTORIZATION AND RECONSTRUCTION
1. Convolution operators on the half line 161
2. Semigroup reconstruction 168
3. Factorization of the symbol 179
4. Construction in a Banach space setting 189
5. Nonregularity of the collision operator 194
Chapter VIII
ALBEDO OPERATORS, H EQUATIONS AND REPRESENTATION OF SOLUTIONS
1. Albedo operators and H equations: the regular case 206
2. Albedo operators and H equations: the singular case 213
3. Reflection and transmission operators and X and Y equations 217
4. Linear H equations, uniqueness properties and constraints 228
5. Addition method 235
Chapter IX
APPLICATIONS OF THE STATIONARY THEORY
1. Radiative transfer without polarization 242
2. Radiative transfer with polarization 256
3. One speed neutron transport 274
4. Multigroup neutron transport 290
5. The Boltzmann equation and BGK equation in rarefied gas dynamics 302
6. A Boltzmann equation for phonon and electron transport 324
Chapter X
INDEFINITE STURM LIOUVILLE PROBLEMS
1. Kinetic equations of Sturm Liouville type 331
2. Half range solutions by eigenfunction expansion 339
3. Reduction to a modified Sturm Liouville problem 342
4. Integral form of Sturm Liouville diffusion problems and factorization 348
5. The Fokker Planck equation 359
6. Electron scattering 362
vii
Chapter XI
TIME DEPENDENT KINETIC EQUATIONS: METHOD OF CHARACTERISTICS
1. Introduction 365
2. The functional formulation 369
3. Vector fields, function spaces and traces 374
4. Existence, uniqueness, dissipativity and positivity in L 384
5. The conservative case 391
6. Existence and uniqueness results in spaces of measures 395
Chapter XII
TIME DEPENDENT KINETIC EQUATIONS: SEMIGROUP APPROACH
1. Introduction and historical remarks 404
2. Existence, uniqueness, dissipativity and positivity in L 407
3. Connection between stationary and time dependent equations 413
4. Spectral properties of positive semigroups 420
5. Spectral and compactness properties for kinetic models 432
Chapter XIII
APPLICATIONS OF THE INITIAL VALUE PROBLEM
1. Kinetic equations in neutron transport 440
2. Neutron transport (continued): spectral decomposition and hydrodynamics 452
3. Spencer Lewis equation and electron deceleration 464
4. Electron drift in a weakly ionized gas 470
5. A transport equation describing growing cell populations 475
Bibliography 480
Subject Index 518
|
| any_adam_object | 1 |
| author | Greenberg, William 1941-2014 Mee, Cornelis van der 1953- Protopopescu, Vladimir |
| author_GND | (DE-588)1255157895 (DE-588)1089353103 (DE-588)1255158050 |
| author_facet | Greenberg, William 1941-2014 Mee, Cornelis van der 1953- Protopopescu, Vladimir |
| author_role | aut aut aut |
| author_sort | Greenberg, William 1941-2014 |
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| dewey-full | 515.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/5 |
| dewey-search | 515.3/5 |
| dewey-sort | 3515.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:16:35Z |
| institution | BVB |
| isbn | 3764317655 0817617655 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000381459 |
| oclc_num | 14905842 |
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| physical | x, 524 Seiten |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Birkhäuser Verlag |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Greenberg, William 1941-2014 (DE-588)1255157895 aut Boundary value problems in abstract kinetic theory W. Greenberg, C. van der Mee, V. Protopopescu Basel ; Boston ; Stuttgart Birkhäuser Verlag 1987 x, 524 Seiten txt rdacontent n rdamedia nc rdacarrier Operator theory 23 Integraalvergelijkingen gtt Operatortheorie gtt Randwaardeproblemen gtt Boundary value problems Initial value problems Kinetic theory of matter Transportprozess (DE-588)4185932-7 gnd rswk-swf Kinetische Theorie (DE-588)4030669-0 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s Kinetische Theorie (DE-588)4030669-0 s DE-604 Transportprozess (DE-588)4185932-7 s Mee, Cornelis van der 1953- (DE-588)1089353103 aut Protopopescu, Vladimir (DE-588)1255158050 aut Operator theory 23 (DE-604)BV000000970 23 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000381459&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Greenberg, William 1941-2014 Mee, Cornelis van der 1953- Protopopescu, Vladimir Boundary value problems in abstract kinetic theory Operator theory Integraalvergelijkingen gtt Operatortheorie gtt Randwaardeproblemen gtt Boundary value problems Initial value problems Kinetic theory of matter Transportprozess (DE-588)4185932-7 gnd Kinetische Theorie (DE-588)4030669-0 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4185932-7 (DE-588)4030669-0 (DE-588)4048395-2 |
| title | Boundary value problems in abstract kinetic theory |
| title_auth | Boundary value problems in abstract kinetic theory |
| title_exact_search | Boundary value problems in abstract kinetic theory |
| title_full | Boundary value problems in abstract kinetic theory W. Greenberg, C. van der Mee, V. Protopopescu |
| title_fullStr | Boundary value problems in abstract kinetic theory W. Greenberg, C. van der Mee, V. Protopopescu |
| title_full_unstemmed | Boundary value problems in abstract kinetic theory W. Greenberg, C. van der Mee, V. Protopopescu |
| title_short | Boundary value problems in abstract kinetic theory |
| title_sort | boundary value problems in abstract kinetic theory |
| topic | Integraalvergelijkingen gtt Operatortheorie gtt Randwaardeproblemen gtt Boundary value problems Initial value problems Kinetic theory of matter Transportprozess (DE-588)4185932-7 gnd Kinetische Theorie (DE-588)4030669-0 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Integraalvergelijkingen Operatortheorie Randwaardeproblemen Boundary value problems Initial value problems Kinetic theory of matter Transportprozess Kinetische Theorie Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000381459&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
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