Many particle dynamics and kinetic equations:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht [u.a.]
Kluwer
1997
|
| Series: | Mathematics and its applications
420 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008038603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | VIII, 244 S. |
| ISBN: | 0792346963 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV011896779 | ||
| 003 | DE-604 | ||
| 005 | 19981103 | ||
| 007 | t| | ||
| 008 | 980420s1997 xx |||| 00||| eng d | ||
| 020 | |a 0792346963 |9 0-7923-4696-3 | ||
| 035 | |a (OCoLC)37293208 | ||
| 035 | |a (DE-599)BVBBV011896779 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 1 | |a eng |h rus | |
| 049 | |a DE-20 |a DE-703 |a DE-29T |a DE-83 |a DE-11 | ||
| 050 | 0 | |a QC174.8 | |
| 082 | 0 | |a 530.13/6 |2 21 | |
| 084 | |a UG 3500 |0 (DE-625)145626: |2 rvk | ||
| 084 | |a PHY 011f |2 stub | ||
| 100 | 1 | |a Cercignani, Carlo |d 1939-2010 |e Verfasser |0 (DE-588)132954184 |4 aut | |
| 245 | 1 | 0 | |a Many particle dynamics and kinetic equations |c by C. Cercignani, V. I. Gerasimenko and D. Ya. Petrina |
| 246 | 1 | 3 | |a Many-particle dynamics and kinetic equations |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1997 | |
| 300 | |a VIII, 244 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 420 | |
| 650 | 7 | |a Dynamica |2 gtt | |
| 650 | 7 | |a Mathematische fysica |2 gtt | |
| 650 | 7 | |a Veel-deeltjes-systemen |2 gtt | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Statistical mechanics | |
| 650 | 4 | |a Transport theory | |
| 650 | 0 | 7 | |a Kinetische Gleichung |0 (DE-588)4030667-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Vielkörperproblem |0 (DE-588)4078900-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Vielkörperproblem |0 (DE-588)4078900-7 |D s |
| 689 | 0 | 1 | |a Kinetische Gleichung |0 (DE-588)4030667-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Gerasimenko, Viktor I. |e Verfasser |4 aut | |
| 700 | 1 | |a Petrina, Dmitrij Ja. |e Verfasser |4 aut | |
| 830 | 0 | |a Mathematics and its applications |v 420 |w (DE-604)BV008163334 |9 420 | |
| 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=008038603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008038603 | |
Record in the Search Index
| _version_ | 1819353581342425088 |
|---|---|
| adam_text | Contents
INTRODUCTION 1
CHAPTER I: THE BBGKY HIERARCHY 7
1.1. Introduction 7
1.2. The Hamilton dynamics of a system of particles with hard core 9
1.2.1. The Hamilton equations 9
1.2.2.Definition of the phase trajectories 12
1.2.3.Existence and some ¦properties of the phase trajectories 11
1.3. The evolution operator for a system with finite number of particles.. 21
1.3.1.Definition of the evolution operator 21
1.3.2.Properties of the evolution operator 23
1.3.3. The initial value problem for the Liouville equation 27
1.3.4 Statistical ensembles 31
1.4. Tiie derivation of the BBGKY hierarchy 33
1 4.1. The distribution functions 33
1.4.2. The BBGKY hierarchy of equations 36
1 4 3.Non symmetrical system of particles: the BBGKY hierarchy 39
1.5. The steady BBGKY hierarchy 44
1.5.1. On the solutions of the steady BBGKY hierarchy 44
1.5.2.Equilibrium distribution functions 45
1.5.3.Equilibrium states of non symmetrical systems 48
1.5.4. The states close to equilibrium 50
Appendix I. The infinitesimal operator of the group S1 (t) 52
Appendix II. The formal derivation of the infinitesimal operator [BB] of the
group SN (t) 61
CHAPTER II: THE INITIAL VALUE PROBLEM FOR THE BBGKY HIERAR¬
CHY OF A SYSTEM OF A FINITE NUMBER OF PARTICLES... 67
2.1. Introduction 67
2.2. The evolution operator of the BBGKY hierarchy 69
2.2.1 .Definitions and basic result . 69
2.2.2.Some auxilary results 71
2.2.3.Properties of the BBGKY evolution operator 75
2.3.Existence of solutions for BBGKY hierarchy 79
2.3.1. The BBGKY hierarchy 79
2.3.2.The existence theorem 80
2.4. Existence of solutions for a one dimensional BBGKY hierarchy 84
2.4 1.Properties of the evolution operator 84
2.4 2.The formula for the solution of the Cauchy problem 92
2 4 3.Existence theorem 93
2 4 4 Sard rod particle system. 95
2.5. The iteration series 97
2.5.1. The construction of the evolution operator for the BBGKY hierarchy by
iteration 97
2.5.2. The explicit form of the iteration series 98
2.5.3.Existence of the iteration series 101
2.5.4 Existence theorem for initial data from some subspace in L1 105
2.5.5. The iteration series for one dimensional hard spheres system 108
CHAPTER III: THE INITIAL VALUE PROBLEM FOR L°° DATA: THERMO
DYNAMIC LIMIT Ill
3.1. Introduction Ill
3.2. A local existence theorem for the BBGKY hierarchy of hard spheresll2
3.2.1.Formulation of problem and existence theorem 112
3.2.2.Basic estimate 113
3.2.3. Other methods of construction of the basic estimate 120
3.2.4 The thermodynamic limit 124
3.3. Global existence theorems 126
3.3.1. The continuation of the solution in time 126
3.3.2. Global existence of a weak solution 127
3.3.3. Global solution for the BBGKY hierarchy of a one dimensional hard
sphere system 130
3.4. Method of the interaction region 135
3 4 1 .Formulation of the problem 135
3.4 2.The interaction region 136
3.4.3.Basic estimate 141
3.4.4.Existence theorems and remarks 145
CHAPTER IV: THE DERIVATION OF THE BOLTZMANN EQUATION ... 153
4.1. Introduction: On the Boltzman Grad limit 153
4.2. The Boltzmann Grad limit for equilibrium states 159
4.2.1. The infinite system of hard spheres 159
4 2.2.Extension: the smooth potential 162
4.3. The Boltzmann hierarchy and the Boltzmaim equation 164
4 3.1. On the Boltzmann hierarchy 164
4.3.2. The main result 167
4 3.3.On the H function and irreversibility concept 167
4.4. The Boltzmann Grad limit for solutions of initial value problem for the
BBGKY hierarchy 172
4 4 1 Auxiliary lemmas 172
4.4 2. The approximating functionals 176
4 4 3. The Boltzmann Grad limit for non equilibrium states 181
4.5. The Boltzmann Grad limit for equilibrium states of systems of hard
spheres in the framework of the canonical ensemble 182
4 5.1 The existence of the Boltzmann Grad limit for normalized equilibrium
distribution functions of hard spheres in the framework of the canonical
ensemble.Statement of the problem 182
4.5.2 The Kirkwood Salsburg equations 185
4.5.3. Estimation of the value a(N. A) 189
4.5.4. The limit of F w 191
4.5.5. The Boltzmann Grad limit for fixed do main A 192
4.5.6 The existence of the Boltzmann Grad limit and thermodynamic limit
for standardly normalized distribution functions on numbers of parti¬
cles 197
4.5.7. The proof of the existence of the limits ofF N R [N), K(2N).
a(N,A)a2 200
4 5.8. The existence of the limit distribution functions for Na2/V = a2 /V =
const 201
4 5.9. The proof of the existence of the limit for F(iV) without scale transfor¬
mation 203
CHAPTER V: ON THE DERIVATION OF KINETIC EQUATIONS FROM
THE BBGKY HIERARCHY 205
5.1. Introduction: kinetic equations 205
5.2. Bogolubov s method of constructing kinetic equations 209
5.2.1. The special solution of the BBGKY hierarchy 209
5.2.2. The general form of a kinetic equation 214
5.2.3.Homogeneous Boltzmann equation 215
5.3. The non equilibrium cluster expansions method 218
5.3.1. A new representation of the BBGKY hierarchy solutions 218
5.3.2. The initial distribution functions with factorization property 220
5.3.3.The comparison with Bogolubov s method 223
5.4. Justification of the generalized kinetic equation 227
5 4 1 The convergence of the kinetic cluster expansion 227
5.4 2.An existence theorem for the generalized kinetic equation 231
5.4 3.The connection between the Boltzmann equation and a stochastic dy¬
namics 232
REFERENCES 233
SUBJECT INDEX 243
|
| any_adam_object | 1 |
| author | Cercignani, Carlo 1939-2010 Gerasimenko, Viktor I. Petrina, Dmitrij Ja |
| author_GND | (DE-588)132954184 |
| author_facet | Cercignani, Carlo 1939-2010 Gerasimenko, Viktor I. Petrina, Dmitrij Ja |
| author_role | aut aut aut |
| author_sort | Cercignani, Carlo 1939-2010 |
| author_variant | c c cc v i g vi vig d j p dj djp |
| building | Verbundindex |
| bvnumber | BV011896779 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.8 |
| callnumber-search | QC174.8 |
| callnumber-sort | QC 3174.8 |
| callnumber-subject | QC - Physics |
| classification_rvk | UG 3500 |
| classification_tum | PHY 011f |
| ctrlnum | (OCoLC)37293208 (DE-599)BVBBV011896779 |
| dewey-full | 530.13/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13/6 |
| dewey-search | 530.13/6 |
| dewey-sort | 3530.13 16 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02027nam a2200517 cb4500</leader><controlfield tag="001">BV011896779</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19981103 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">980420s1997 xx |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0792346963</subfield><subfield code="9">0-7923-4696-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)37293208</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011896779</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="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">rus</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QC174.8</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">530.13/6</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UG 3500</subfield><subfield code="0">(DE-625)145626:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 011f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Cercignani, Carlo</subfield><subfield code="d">1939-2010</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)132954184</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Many particle dynamics and kinetic equations</subfield><subfield code="c">by C. Cercignani, V. I. Gerasimenko and D. Ya. Petrina</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Many-particle dynamics and kinetic equations</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht [u.a.]</subfield><subfield code="b">Kluwer</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 244 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="490" ind1="1" ind2=" "><subfield code="a">Mathematics and its applications</subfield><subfield code="v">420</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Dynamica</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Mathematische fysica</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Veel-deeltjes-systemen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematische Physik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Statistical mechanics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Transport theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kinetische Gleichung</subfield><subfield code="0">(DE-588)4030667-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Vielkörperproblem</subfield><subfield code="0">(DE-588)4078900-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Vielkörperproblem</subfield><subfield code="0">(DE-588)4078900-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Kinetische Gleichung</subfield><subfield code="0">(DE-588)4030667-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gerasimenko, Viktor I.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Petrina, Dmitrij Ja.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematics and its applications</subfield><subfield code="v">420</subfield><subfield code="w">(DE-604)BV008163334</subfield><subfield code="9">420</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=008038603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-008038603</subfield></datafield></record></collection> |
| id | DE-604.BV011896779 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:20:44Z |
| institution | BVB |
| isbn | 0792346963 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008038603 |
| oclc_num | 37293208 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-29T DE-83 DE-11 |
| owner_facet | DE-20 DE-703 DE-29T DE-83 DE-11 |
| physical | VIII, 244 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spellingShingle | Cercignani, Carlo 1939-2010 Gerasimenko, Viktor I. Petrina, Dmitrij Ja Many particle dynamics and kinetic equations Mathematics and its applications Dynamica gtt Mathematische fysica gtt Veel-deeltjes-systemen gtt Mathematische Physik Mathematical physics Statistical mechanics Transport theory Kinetische Gleichung (DE-588)4030667-7 gnd Vielkörperproblem (DE-588)4078900-7 gnd |
| subject_GND | (DE-588)4030667-7 (DE-588)4078900-7 |
| title | Many particle dynamics and kinetic equations |
| title_alt | Many-particle dynamics and kinetic equations |
| title_auth | Many particle dynamics and kinetic equations |
| title_exact_search | Many particle dynamics and kinetic equations |
| title_full | Many particle dynamics and kinetic equations by C. Cercignani, V. I. Gerasimenko and D. Ya. Petrina |
| title_fullStr | Many particle dynamics and kinetic equations by C. Cercignani, V. I. Gerasimenko and D. Ya. Petrina |
| title_full_unstemmed | Many particle dynamics and kinetic equations by C. Cercignani, V. I. Gerasimenko and D. Ya. Petrina |
| title_short | Many particle dynamics and kinetic equations |
| title_sort | many particle dynamics and kinetic equations |
| topic | Dynamica gtt Mathematische fysica gtt Veel-deeltjes-systemen gtt Mathematische Physik Mathematical physics Statistical mechanics Transport theory Kinetische Gleichung (DE-588)4030667-7 gnd Vielkörperproblem (DE-588)4078900-7 gnd |
| topic_facet | Dynamica Mathematische fysica Veel-deeltjes-systemen Mathematische Physik Mathematical physics Statistical mechanics Transport theory Kinetische Gleichung Vielkörperproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008038603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT cercignanicarlo manyparticledynamicsandkineticequations AT gerasimenkoviktori manyparticledynamicsandkineticequations AT petrinadmitrijja manyparticledynamicsandkineticequations |