Lecture notes on the mathematical theory of the Boltzmann equation:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore u.a.
World Scientific
1995
|
| Schriftenreihe: | Series on advances in mathematics for applied sciences
33 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 255 S. |
| ISBN: | 9810221665 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010908405 | ||
| 003 | DE-604 | ||
| 005 | 20020715 | ||
| 007 | t | ||
| 008 | 960822s1995 |||| 00||| eng d | ||
| 020 | |a 9810221665 |9 981-02-2166-5 | ||
| 035 | |a (OCoLC)32271891 | ||
| 035 | |a (DE-599)BVBBV010908405 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-19 |a DE-20 |a DE-11 | ||
| 050 | 0 | |a QC175.2 | |
| 082 | 0 | |a 530.1/38 |2 20 | |
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 245 | 1 | 0 | |a Lecture notes on the mathematical theory of the Boltzmann equation |c ed. N. Bellomo. Contrib. L. Arlotti ... |
| 264 | 1 | |a Singapore u.a. |b World Scientific |c 1995 | |
| 300 | |a X, 255 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 33 | |
| 650 | 7 | |a Transport, théorie du |2 ram | |
| 650 | 4 | |a Transport theory | |
| 650 | 0 | 7 | |a Boltzmann-Gleichung |0 (DE-588)4146261-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kinetische Gleichung |0 (DE-588)4030667-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare partielle Differentialgleichung |0 (DE-588)4128900-6 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4143413-4 |a Aufsatzsammlung |2 gnd-content | |
| 689 | 0 | 0 | |a Boltzmann-Gleichung |0 (DE-588)4146261-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Nichtlineare partielle Differentialgleichung |0 (DE-588)4128900-6 |D s |
| 689 | 1 | 1 | |a Kinetische Gleichung |0 (DE-588)4030667-7 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Bellomo, Nicola |d 1943- |e Sonstige |0 (DE-588)11304206X |4 oth | |
| 700 | 1 | |a Arlotti, L. |e Sonstige |4 oth | |
| 830 | 0 | |a Series on advances in mathematics for applied sciences |v 33 |w (DE-604)BV004569239 |9 33 | |
| 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=007296628&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007296628 | ||
Datensatz im Suchindex
| _version_ | 1804125400190681088 |
|---|---|
| adam_text | CONTENTS
Preface v
Lecture 1 by L. Arlotti and N. Bellomo
On the Cauchy Problem for the Boltzmann Equation
1 The Nonlinear Boltzmann Equation 1
2 On the Initial Value Problem in the Absence of External
Force Field 4
2.1 The Cauchy Problem for Small Initial Data 7
2.2 The Cauchy Problem for Large Initial Data .... 18
2.3 The Cauchy Problem Near Equilibrium 31
3 On the Generalized Boltzmann Equation 34
4 Open Problems 42
4.1 On the Cauchy Problem with External Force Field . 42
4.2 On the Cauchy Problem Related to Wave Phenomena 44
4.3 On the Cauchy Problem Related to Hydrodynamics 46
4.4 On the Cauchy Problem for the Discrete Boltzmann
equation 47
4.5 On the Cauchy Problem for Nonlinear
Continuous Models 50
5 Final Remarks 52
References 54
vii
viii CONTENTS
Lecture 2 by M. Lachowicz
Asymptotic Analysis of Nonlinear Kinetic Equations:
The Hydrodynamic Limit
1 Introduction 65
2 Kinetic and Hydrodynamic Equations 67
2.1 Kinetic Equations 67
2.2 Dimension Analysis 74
2.3 Hydrodynamic Equations 76
2.4 Notations 79
2.5 Basic Estimates 84
3. Compressible Dynamics 86
3.1 Singularly Perturbed Boltzmann Equation .... 86
3.2 Hilbert Procedure 88
3.3 Modified Hilbert Expansion 92
3.4 Initial Layer Expansion 95
3.5 Equation for the Remainder 98
3.6 Hydrodynamic Limit for the Boltzmann Equation . 105
3.7 Hydrodynamic Limit for the Enskog Equation for
a e 106
3.8 Hydrodynamic Limit for the Enskog Equation for
a~e 116
3.9 Hydrodynamic Limit for the Povzner Equation. . . 120
3.10 SDE Approximating Solutions of the Hydrodynamic
Equations 121
4. Incompressible Dynamics 130
4.1 Level of Smooth Solutions 130
4.2 Level of Weak Solutions 133
References 137
CONTENTS ix
Lecture 3 by J. Polewczak
An Introduction to Kinetic Theory of Dense Gases
1 Introduction 149
2 The Revised Enskog Equation 151
3 The Square Well Kinetic Equation 160
References 176
Lecture 4 by W. Walus
Computational Methods for the
Boltzmann Equation
1 Introduction 179
2 The Splitting Method in Kinetic Theory 184
3 Numerical Schemes for the Boltzmann Equation . . . 188
4 Numerical Evaluation of the Collision Operator . . . 194
5 Correction Techniques 205
6 Other Methods 206
References 213
General Bibliography
Books and Lecture Notes Kinetic Theory 225
Books and Lecture Notes Fluid Dynamics 226
x CONTENTS
Books and Lecture Notes Mathematical Methods . . 227
Review Papers 228
Research Papers Cauchy Problem 230
Research Papers Derivation of Kinetic Equations . . 234
Research Papers Discrete Boltzmann Equation . . . 234
Research Papers Enskog Equation 237
Research Papers Hydrodynamics and Asymptotic
Methods 238
Research Papers Mathematical Methods 242
Research Papers Nonlinear Models 243
Research Papers Numerical Schemes 244
Research Papers Problems with Boundaries .... 253
Research Papers Wave Solutions 255
|
| any_adam_object | 1 |
| author_GND | (DE-588)11304206X |
| building | Verbundindex |
| bvnumber | BV010908405 |
| callnumber-first | Q - Science |
| callnumber-label | QC175 |
| callnumber-raw | QC175.2 |
| callnumber-search | QC175.2 |
| callnumber-sort | QC 3175.2 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 540 SK 950 |
| ctrlnum | (OCoLC)32271891 (DE-599)BVBBV010908405 |
| dewey-full | 530.1/38 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/38 |
| dewey-search | 530.1/38 |
| dewey-sort | 3530.1 238 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02037nam a2200481 cb4500</leader><controlfield tag="001">BV010908405</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20020715 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">960822s1995 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9810221665</subfield><subfield code="9">981-02-2166-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)32271891</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010908405</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-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QC175.2</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">530.1/38</subfield><subfield code="2">20</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="245" ind1="1" ind2="0"><subfield code="a">Lecture notes on the mathematical theory of the Boltzmann equation</subfield><subfield code="c">ed. N. Bellomo. Contrib. L. Arlotti ...</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore u.a.</subfield><subfield code="b">World Scientific</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 255 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">Series on advances in mathematics for applied sciences</subfield><subfield code="v">33</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Transport, théorie du</subfield><subfield code="2">ram</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">Boltzmann-Gleichung</subfield><subfield code="0">(DE-588)4146261-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</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">Nichtlineare partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4128900-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4143413-4</subfield><subfield code="a">Aufsatzsammlung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Boltzmann-Gleichung</subfield><subfield code="0">(DE-588)4146261-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Nichtlineare partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4128900-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" 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="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Bellomo, Nicola</subfield><subfield code="d">1943-</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)11304206X</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Arlotti, L.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Series on advances in mathematics for applied sciences</subfield><subfield code="v">33</subfield><subfield code="w">(DE-604)BV004569239</subfield><subfield code="9">33</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=007296628&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:BVB01-007296628</subfield></datafield></record></collection> |
| genre | (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Aufsatzsammlung |
| id | DE-604.BV010908405 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:00:57Z |
| institution | BVB |
| isbn | 9810221665 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007296628 |
| oclc_num | 32271891 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-19 DE-BY-UBM DE-20 DE-11 |
| owner_facet | DE-384 DE-703 DE-19 DE-BY-UBM DE-20 DE-11 |
| physical | X, 255 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 | Lecture notes on the mathematical theory of the Boltzmann equation ed. N. Bellomo. Contrib. L. Arlotti ... Singapore u.a. World Scientific 1995 X, 255 S. txt rdacontent n rdamedia nc rdacarrier Series on advances in mathematics for applied sciences 33 Transport, théorie du ram Transport theory Boltzmann-Gleichung (DE-588)4146261-0 gnd rswk-swf Kinetische Gleichung (DE-588)4030667-7 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Boltzmann-Gleichung (DE-588)4146261-0 s DE-604 Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Kinetische Gleichung (DE-588)4030667-7 s Bellomo, Nicola 1943- Sonstige (DE-588)11304206X oth Arlotti, L. Sonstige oth Series on advances in mathematics for applied sciences 33 (DE-604)BV004569239 33 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007296628&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lecture notes on the mathematical theory of the Boltzmann equation Series on advances in mathematics for applied sciences Transport, théorie du ram Transport theory Boltzmann-Gleichung (DE-588)4146261-0 gnd Kinetische Gleichung (DE-588)4030667-7 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4146261-0 (DE-588)4030667-7 (DE-588)4128900-6 (DE-588)4143413-4 |
| title | Lecture notes on the mathematical theory of the Boltzmann equation |
| title_auth | Lecture notes on the mathematical theory of the Boltzmann equation |
| title_exact_search | Lecture notes on the mathematical theory of the Boltzmann equation |
| title_full | Lecture notes on the mathematical theory of the Boltzmann equation ed. N. Bellomo. Contrib. L. Arlotti ... |
| title_fullStr | Lecture notes on the mathematical theory of the Boltzmann equation ed. N. Bellomo. Contrib. L. Arlotti ... |
| title_full_unstemmed | Lecture notes on the mathematical theory of the Boltzmann equation ed. N. Bellomo. Contrib. L. Arlotti ... |
| title_short | Lecture notes on the mathematical theory of the Boltzmann equation |
| title_sort | lecture notes on the mathematical theory of the boltzmann equation |
| topic | Transport, théorie du ram Transport theory Boltzmann-Gleichung (DE-588)4146261-0 gnd Kinetische Gleichung (DE-588)4030667-7 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Transport, théorie du Transport theory Boltzmann-Gleichung Kinetische Gleichung Nichtlineare partielle Differentialgleichung Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007296628&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004569239 |
| work_keys_str_mv | AT bellomonicola lecturenotesonthemathematicaltheoryoftheboltzmannequation AT arlottil lecturenotesonthemathematicaltheoryoftheboltzmannequation |