The Cauchy problem in kinetic theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia, Pa.
SIAM
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 241 S. |
| ISBN: | 0898713676 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV011050172 | ||
| 003 | DE-604 | ||
| 005 | 20200122 | ||
| 007 | t | ||
| 008 | 961111s1996 |||| 00||| engod | ||
| 020 | |a 0898713676 |9 0-89871-367-6 | ||
| 035 | |a (OCoLC)633926360 | ||
| 035 | |a (DE-599)BVBBV011050172 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-19 |a DE-706 |a DE-11 |a DE-384 | ||
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a UG 3100 |0 (DE-625)145625: |2 rvk | ||
| 084 | |a MAT 355f |2 stub | ||
| 100 | 1 | |a Glassey, Robert |d 1946-2020 |e Verfasser |0 (DE-588)1203407009 |4 aut | |
| 245 | 1 | 0 | |a The Cauchy problem in kinetic theory |c Robert T. Glassey |
| 264 | 1 | |a Philadelphia, Pa. |b SIAM |c 1996 | |
| 300 | |a XII, 241 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Kinetische Theorie |0 (DE-588)4030669-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Cauchy-Anfangswertproblem |0 (DE-588)4147404-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Cauchy-Anfangswertproblem |0 (DE-588)4147404-1 |D s |
| 689 | 0 | 1 | |a Kinetische Theorie |0 (DE-588)4030669-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007400567&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007400567 | ||
Record in the Search Index
| _version_ | 1804125540045553664 |
|---|---|
| adam_text | Contents
Preface ix
CHAPTER 1. Properties of the Collision Operator 1
1.1 Kinetic Theory. Derivation of the Equations 1
1.2 The Form of the Collision Operator 5
1.3 The Hard Sphere Case 7
1.4 Conservation Laws and the Entropy 9
1.5 Relevance of the Maxwellian 12
1.6 The Jacobian Determinant 15
1.7 The Structure of Collision Invariants 1G
1.8 Relationship of the Boltzmann Equation to the
Equations of Fluids 20
References 22
CHAPTER 2. The Boltzmann Equation Near the Vacuum 25
2.1 Invariance of x tv 2 + x ~ tu 2 25
2.2 Sequences of Approximate Solutions 31
2.3 Satisfaction of the Beginning Condition 33
2.4 Proof that u = ( 35
2.5 Remarks and Related Questions 36
References 37
CHAPTER 3. The Boltzmann Equation Near the Equilibrium 39
3.1 The Perturbation from Equilibrium 39
3.2 Computation of the Integral Operator 40
3.3 Estimates on the Integral Operator 47
v
vi CONTENTS
3.4 Properties of L 51
3.5 Compactness of K 54
3.6 Solution Spaces 56
3.7 An Orthonormal Basis for N(L) 58
3.8 Estimates on the Nonlinear Term 60
3.9 Equations for 13 Moments 65
3.10 Computation of the Coefficient Matrices 70
3.11 Compensating Functions 75
3.12 Time Decay Estimates 81
3.13 Time Decay in Other Norms 86
3.14 The Major Theorem 92
3.15 The Relativistic Boltzmann Equation 94
References 113
CHAPTER 4. The Vlasov Poisson System 117
4.1 Introduction 117
4.2 Preliminaries and A Priori Estimates 118
4.3 Sketch of the Existence Proof 125
4.4 The Good, the Bad and the Ugly 125
4.5 The Bound on the Velocity Support 131
4.6 Blow up in the Gravitational Case 133
References 136
CHAPTER 5. The Vlasov Maxwell System 139
5.1 Collisionless Plasmas 139
5.2 Control of Large Velocities 140
5.3 Representation of the Fields 141
5.4 Representation of the Derivatives of the Fields 144
5.5 Estimates on the Particle Density 147
5.6 Bounds on the Field 148
5.7 Bounds on the Gradient of the Field 149
5.8 Proof of Existence 152
References 159
CHAPTER 6. Dilute Collisionless Plasmas 163
6.1 The Small data Theorem 163
6.2 Outline of the Proof 165
6.3 Characteristics 167
6.4 The Particle Densities 171
6.5 Estimates on the Fields 173
6.6 Estimates on Derivatives of the Fields 177
References 181
CONTENTS vii
CHAPTER 7. Velocity Averages: Weak Solutions to the
Vlasov Maxwell System 185
7.1 Sketch of the Problem 185
7.2 The Velocity Averaging Smoothing Effect 187
7.3 Convergence of the Current Density 192
7.4 Completion of the Proof 198
References 200
CHAPTER 8. Convergence of a Particle Method for the
Vlasov Maxwell System 203
8.1 Introduction 203
8.2 The Particle Simulation 206
8.3 The Field Errors 212
8.4 The Particle Errors 225
8.5 Summing the Errors 229
References 232
Index 235
|
| any_adam_object | 1 |
| author | Glassey, Robert 1946-2020 |
| author_GND | (DE-588)1203407009 |
| author_facet | Glassey, Robert 1946-2020 |
| author_role | aut |
| author_sort | Glassey, Robert 1946-2020 |
| author_variant | r g rg |
| building | Verbundindex |
| bvnumber | BV011050172 |
| classification_rvk | SK 540 SK 950 UG 3100 |
| classification_tum | MAT 355f |
| ctrlnum | (OCoLC)633926360 (DE-599)BVBBV011050172 |
| discipline | Physik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01462nam a2200373 c 4500</leader><controlfield tag="001">BV011050172</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200122 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">961111s1996 |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0898713676</subfield><subfield code="9">0-89871-367-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)633926360</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011050172</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-384</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 540</subfield><subfield code="0">(DE-625)143245:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UG 3100</subfield><subfield code="0">(DE-625)145625:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 355f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Glassey, Robert</subfield><subfield code="d">1946-2020</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1203407009</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Cauchy problem in kinetic theory</subfield><subfield code="c">Robert T. Glassey</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Philadelphia, Pa.</subfield><subfield code="b">SIAM</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XII, 241 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kinetische Theorie</subfield><subfield code="0">(DE-588)4030669-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Cauchy-Anfangswertproblem</subfield><subfield code="0">(DE-588)4147404-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Cauchy-Anfangswertproblem</subfield><subfield code="0">(DE-588)4147404-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Kinetische Theorie</subfield><subfield code="0">(DE-588)4030669-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007400567&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007400567</subfield></datafield></record></collection> |
| id | DE-604.BV011050172 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:03:11Z |
| institution | BVB |
| isbn | 0898713676 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007400567 |
| oclc_num | 633926360 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-706 DE-11 DE-384 |
| owner_facet | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-706 DE-11 DE-384 |
| physical | XII, 241 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | SIAM |
| record_format | marc |
| spelling | Glassey, Robert 1946-2020 Verfasser (DE-588)1203407009 aut The Cauchy problem in kinetic theory Robert T. Glassey Philadelphia, Pa. SIAM 1996 XII, 241 S. txt rdacontent n rdamedia nc rdacarrier Kinetische Theorie (DE-588)4030669-0 gnd rswk-swf Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd rswk-swf Cauchy-Anfangswertproblem (DE-588)4147404-1 s Kinetische Theorie (DE-588)4030669-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007400567&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Glassey, Robert 1946-2020 The Cauchy problem in kinetic theory Kinetische Theorie (DE-588)4030669-0 gnd Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd |
| subject_GND | (DE-588)4030669-0 (DE-588)4147404-1 |
| title | The Cauchy problem in kinetic theory |
| title_auth | The Cauchy problem in kinetic theory |
| title_exact_search | The Cauchy problem in kinetic theory |
| title_full | The Cauchy problem in kinetic theory Robert T. Glassey |
| title_fullStr | The Cauchy problem in kinetic theory Robert T. Glassey |
| title_full_unstemmed | The Cauchy problem in kinetic theory Robert T. Glassey |
| title_short | The Cauchy problem in kinetic theory |
| title_sort | the cauchy problem in kinetic theory |
| topic | Kinetische Theorie (DE-588)4030669-0 gnd Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd |
| topic_facet | Kinetische Theorie Cauchy-Anfangswertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007400567&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT glasseyrobert thecauchyprobleminkinetictheory |