Singularly perturbed evolution equations with applications to kinetic theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore u.a.
World Scientific
1995
|
| Series: | Series on advances in mathematics for applied sciences
34 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 310 S. |
| ISBN: | 9810221258 |
Staff View
MARC
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| 245 | 1 | 0 | |a Singularly perturbed evolution equations with applications to kinetic theory |c J. R. Mika & J. Banasiak |
| 264 | 1 | |a Singapore u.a. |b World Scientific |c 1995 | |
| 300 | |a IX, 310 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on advances in mathematics for applied sciences |v 34 | |
| 650 | 7 | |a Dynamica |2 gtt | |
| 650 | 7 | |a Evolutionaire vergelijkingen |2 gtt | |
| 650 | 7 | |a Peturbations singulières (mathématiques) |2 ram | |
| 650 | 7 | |a Storingsrekening |2 gtt | |
| 650 | 4 | |a Evolution equations | |
| 650 | 4 | |a Kinetic theory of matter | |
| 650 | 4 | |a Perturbation (Mathematics) | |
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| 700 | 1 | |a Banasiak, Jacek |e Verfasser |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
1 Introduction 1
2 Mathematical preliminaries 7
1 Introduction 7
2 General definitions and notation 7
3 Banach and Hilbert spaces 10
4 Distributions and Sobolev spaces 19
5 Vector valued functions 28
6 Unbounded operators 32
7 Elements of spectral theory 41
3 Semigroup theory 61
1 Introduction 61
2 Generation of semigroups 62
3 Fractional powers of closed operators 72
4 Perturbation theorems 76
5 Asymptotic behaviour of solutions 82
6 Inhomogeneous Cauchy problem 86
7 Applications to partial differential equations 93
vii
viii CONTENTS
4 Development of asymptotic methods for singularly perturbed evo¬
lution equations 105
1 Introduction 105
2 Single evolution equations with a small parameter 107
3 Systems of evolution equations with a small parameter Ill
5 Some singular singularly perturbed evolution equations and kinetic
equation 125
1 Singular singularly perturbed evolution equations 125
2 Model system: exact solution 133
3 Model system: standard asymptotic analysis 136
4 Model system: compressed asymptotic expansion 139
5 Modified model system 143
6 Singular singularly perturbed evolution equations: compressed approach 148
7 Singularly perturbed linear kinetic equations 151
6 Hilbert space theory for equations of kinetic type 161
1 Introduction 161
2 Preliminary results 162
3 Properties of terms of expansion 168
4 Estimates of error of asymptotic expansion 179
5 Remarks on non selfadjointness of C 192
7 Applications to kinetic equations with bounded collision operators 197
1 Introduction 197
2 Properties of linear Boltzmann equation with unbounded velocity range 199
3 Diffusion approximation to linear Boltzmann equation 207
8 Applications to equations of Fokker Planck type 215
1 Introduction 215
2 General assumptions 219
3 Variational setting 222
4 Fokker Planck equation of electron scattering in plasma 224
CONTENTS ix
5 Fokker Planck equation of Brownian motion 228
6 Fokker Planck equation of vibrational relaxation of harmonic oscillator 234
9 Applications to spatially inhomogeneous linear Boltzmann equation239
1 Introduction 239
2 Properties of neutron transport equation in slab geometry 240
3 Asymptotic expansion 246
4 Remarks on general spatially inhomogeneous equation 254
10 Application to kinetic equation with external field 257
1 Introduction 257
2 Properties of collision operator 260
3 Formal asymptotic formulae 263
4 Initial layer part 267
5 Bulk part 271
6 Error of asymptotic expansion 276
11 Miscellaneous results 279
1 Introduction 279
2 Asymptotic analysis of telegraph systems 279
3 Remarks on compressed asymptotic method in insetting 290
4 Carleman model 294
Bibliography 301
Index 309
|
| any_adam_object | 1 |
| author | Mika, Janusz Banasiak, Jacek |
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| 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 |
| format | Book |
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| id | DE-604.BV011283838 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:07:07Z |
| institution | BVB |
| isbn | 9810221258 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007577534 |
| oclc_num | 32746102 |
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| owner_facet | DE-384 DE-703 DE-11 |
| physical | IX, 310 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| 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 | Mika, Janusz Verfasser aut Singularly perturbed evolution equations with applications to kinetic theory J. R. Mika & J. Banasiak Singapore u.a. World Scientific 1995 IX, 310 S. txt rdacontent n rdamedia nc rdacarrier Series on advances in mathematics for applied sciences 34 Dynamica gtt Evolutionaire vergelijkingen gtt Peturbations singulières (mathématiques) ram Storingsrekening gtt Evolution equations Kinetic theory of matter Perturbation (Mathematics) Singuläre Störung (DE-588)4055100-3 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 s Singuläre Störung (DE-588)4055100-3 s DE-604 Banasiak, Jacek Verfasser aut Series on advances in mathematics for applied sciences 34 (DE-604)BV004569239 34 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007577534&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mika, Janusz Banasiak, Jacek Singularly perturbed evolution equations with applications to kinetic theory Series on advances in mathematics for applied sciences Dynamica gtt Evolutionaire vergelijkingen gtt Peturbations singulières (mathématiques) ram Storingsrekening gtt Evolution equations Kinetic theory of matter Perturbation (Mathematics) Singuläre Störung (DE-588)4055100-3 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4055100-3 (DE-588)4129061-6 |
| title | Singularly perturbed evolution equations with applications to kinetic theory |
| title_auth | Singularly perturbed evolution equations with applications to kinetic theory |
| title_exact_search | Singularly perturbed evolution equations with applications to kinetic theory |
| title_full | Singularly perturbed evolution equations with applications to kinetic theory J. R. Mika & J. Banasiak |
| title_fullStr | Singularly perturbed evolution equations with applications to kinetic theory J. R. Mika & J. Banasiak |
| title_full_unstemmed | Singularly perturbed evolution equations with applications to kinetic theory J. R. Mika & J. Banasiak |
| title_short | Singularly perturbed evolution equations with applications to kinetic theory |
| title_sort | singularly perturbed evolution equations with applications to kinetic theory |
| topic | Dynamica gtt Evolutionaire vergelijkingen gtt Peturbations singulières (mathématiques) ram Storingsrekening gtt Evolution equations Kinetic theory of matter Perturbation (Mathematics) Singuläre Störung (DE-588)4055100-3 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Dynamica Evolutionaire vergelijkingen Peturbations singulières (mathématiques) Storingsrekening Evolution equations Kinetic theory of matter Perturbation (Mathematics) Singuläre Störung Evolutionsgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007577534&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004569239 |
| work_keys_str_mv | AT mikajanusz singularlyperturbedevolutionequationswithapplicationstokinetictheory AT banasiakjacek singularlyperturbedevolutionequationswithapplicationstokinetictheory |