Scaling Limits and Models in Physical Processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1998
|
| Schriftenreihe: | DMV Seminar
28 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The first part of this volume presents the basic ideas concerning perturbation and scaling methods in the mathematical theory of dilute gases, based on Boltzmann's integro-differential equation. It is of course impossible to cover the developments of this subject in less than one hundred pages. Already in 1912 none less than David Hilbert indicated how to obtain approximate solutions of the scaled Boltzmann equation in the form of a perturbation of a parameter inversely proportional to the gas density. His paper is also reprinted as Chapter XXII of his treatise Grundzuge einer allgemeinen Theorie der linearen Integralgleichungen. The motive for this circumstance is clearly stated in the preface to that book ("Recently I have added, to conclude, a new chapter on the kinetic theory of gases. [ . . . ]. I recognize in the theory of gases the most splendid application of the theorems concerning integral equations. ") The mathematically rigorous theory started, however, in 1933 with a paper [48] by Tage Gillis Torsten Carleman, who proved a theorem of global existence and uniqueness for a gas of hard spheres in the so-called space-homogeneous case. Many other results followed; those based on perturbation and scaling methods will be dealt with in some detail. Here, I cannot refrain from mentioning that, when Pierre-Louis Lions obtained the Fields medal (1994), the commendation quoted explicitly his work with the late Ronald DiPerna on the existence of solutions of the Boltzmann equation |
| Beschreibung: | 1 Online-Ressource (VI, 194 p.) 2 illus |
| ISBN: | 9783034888103 9783764359850 |
| DOI: | 10.1007/978-3-0348-8810-3 |
Internformat
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| 500 | |a The first part of this volume presents the basic ideas concerning perturbation and scaling methods in the mathematical theory of dilute gases, based on Boltzmann's integro-differential equation. It is of course impossible to cover the developments of this subject in less than one hundred pages. Already in 1912 none less than David Hilbert indicated how to obtain approximate solutions of the scaled Boltzmann equation in the form of a perturbation of a parameter inversely proportional to the gas density. His paper is also reprinted as Chapter XXII of his treatise Grundzuge einer allgemeinen Theorie der linearen Integralgleichungen. The motive for this circumstance is clearly stated in the preface to that book ("Recently I have added, to conclude, a new chapter on the kinetic theory of gases. [ . . . ]. I recognize in the theory of gases the most splendid application of the theorems concerning integral equations. ") The mathematically rigorous theory started, however, in 1933 with a paper [48] by Tage Gillis Torsten Carleman, who proved a theorem of global existence and uniqueness for a gas of hard spheres in the so-called space-homogeneous case. Many other results followed; those based on perturbation and scaling methods will be dealt with in some detail. Here, I cannot refrain from mentioning that, when Pierre-Louis Lions obtained the Fields medal (1994), the commendation quoted explicitly his work with the late Ronald DiPerna on the existence of solutions of the Boltzmann equation | ||
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Datensatz im Suchindex
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| author | Cercignani, Carlo 1939-2010 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8810-3 |
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| language | English |
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| spelling | Cercignani, Carlo 1939-2010 Verfasser (DE-588)132954184 aut Scaling Limits and Models in Physical Processes by Carlo Cercignani, David H. Sattinger Basel Birkhäuser Basel 1998 1 Online-Ressource (VI, 194 p.) 2 illus txt rdacontent c rdamedia cr rdacarrier DMV Seminar 28 The first part of this volume presents the basic ideas concerning perturbation and scaling methods in the mathematical theory of dilute gases, based on Boltzmann's integro-differential equation. It is of course impossible to cover the developments of this subject in less than one hundred pages. Already in 1912 none less than David Hilbert indicated how to obtain approximate solutions of the scaled Boltzmann equation in the form of a perturbation of a parameter inversely proportional to the gas density. His paper is also reprinted as Chapter XXII of his treatise Grundzuge einer allgemeinen Theorie der linearen Integralgleichungen. The motive for this circumstance is clearly stated in the preface to that book ("Recently I have added, to conclude, a new chapter on the kinetic theory of gases. [ . . . ]. I recognize in the theory of gases the most splendid application of the theorems concerning integral equations. ") The mathematically rigorous theory started, however, in 1933 with a paper [48] by Tage Gillis Torsten Carleman, who proved a theorem of global existence and uniqueness for a gas of hard spheres in the so-called space-homogeneous case. Many other results followed; those based on perturbation and scaling methods will be dealt with in some detail. Here, I cannot refrain from mentioning that, when Pierre-Louis Lions obtained the Fields medal (1994), the commendation quoted explicitly his work with the late Ronald DiPerna on the existence of solutions of the Boltzmann equation Mathematics Mathematics, general Mathematik Kinetische Gastheorie (DE-588)4163881-5 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Integrables System (DE-588)4114032-1 gnd rswk-swf Skalierungsgesetz (DE-588)4205012-1 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Integrables System (DE-588)4114032-1 s 1\p DE-604 Kinetische Gastheorie (DE-588)4163881-5 s Skalierungsgesetz (DE-588)4205012-1 s 2\p DE-604 Sattinger, David H. Sonstige oth DMV Seminar 28 (DE-604)BV000020322 28 https://doi.org/10.1007/978-3-0348-8810-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cercignani, Carlo 1939-2010 Scaling Limits and Models in Physical Processes DMV Seminar Mathematics Mathematics, general Mathematik Kinetische Gastheorie (DE-588)4163881-5 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Integrables System (DE-588)4114032-1 gnd Skalierungsgesetz (DE-588)4205012-1 gnd |
| subject_GND | (DE-588)4163881-5 (DE-588)4128900-6 (DE-588)4114032-1 (DE-588)4205012-1 |
| title | Scaling Limits and Models in Physical Processes |
| title_auth | Scaling Limits and Models in Physical Processes |
| title_exact_search | Scaling Limits and Models in Physical Processes |
| title_full | Scaling Limits and Models in Physical Processes by Carlo Cercignani, David H. Sattinger |
| title_fullStr | Scaling Limits and Models in Physical Processes by Carlo Cercignani, David H. Sattinger |
| title_full_unstemmed | Scaling Limits and Models in Physical Processes by Carlo Cercignani, David H. Sattinger |
| title_short | Scaling Limits and Models in Physical Processes |
| title_sort | scaling limits and models in physical processes |
| topic | Mathematics Mathematics, general Mathematik Kinetische Gastheorie (DE-588)4163881-5 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Integrables System (DE-588)4114032-1 gnd Skalierungsgesetz (DE-588)4205012-1 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Kinetische Gastheorie Nichtlineare partielle Differentialgleichung Integrables System Skalierungsgesetz |
| url | https://doi.org/10.1007/978-3-0348-8810-3 |
| volume_link | (DE-604)BV000020322 |
| work_keys_str_mv | AT cercignanicarlo scalinglimitsandmodelsinphysicalprocesses AT sattingerdavidh scalinglimitsandmodelsinphysicalprocesses |