Scaling Limits and Models in Physical Processes (Paperback)
Carlo Cercignani
ISBN 10: 3764359854 ISBN 13: 9783764359850
Editorial: Birkhauser Verlag AG, Basel, 1998
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Paperback. 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 exis- tence 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 meth- ods will be dealt with in some detail. Here, I cannot refrain from mentioning that, when Pierre-Louis Lions obtained the Fields medal (1994), the commenda- tion quoted explicitly his work with the late Ronald DiPerna on the existence of solutions of the Boltzmann equation. This is an introductory text, for students and non-specialists, on the role of integrable systems for modelling weakly non-linear equations which contain the effects of both dispersion and nonlinearity. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. N° de ref. del artículo 9783764359850
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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 exis tence 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 meth ods will be dealt with in some detail. Here, I cannot refrain from mentioning that, when Pierre-Louis Lions obtained the Fields medal (1994), the commenda tion quoted explicitly his work with the late Ronald DiPerna on the existence of solutions of the Boltzmann equation.
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Título: Scaling Limits and Models in Physical ...
Editorial: Birkhauser Verlag AG, Basel
Año de publicación: 1998
Encuadernación: Paperback
Condición: new
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. I Scaling and Mathematical Models in Kinetic Theory.- 1 Boltzmann Equation and Gas Surface Interaction.- 1.1 Introduction.- 1.2 The Boltzmann equation.- 1.3 Molecules different from hard spheres.- 1.4 Collision invariants.- 1.5 The Boltzmann inequality and . Nº de ref. del artículo: 5279245
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Taschenbuch. Condición: Neu. Scaling Limits and Models in Physical Processes | David Sattinger (u. a.) | Taschenbuch | vi | Englisch | 1998 | Birkhäuser | EAN 9783764359850 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Nº de ref. del artículo: 101828609
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Taschenbuch. Condición: Neu. Neuware -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 exis tence 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 meth ods will be dealt with in some detail. Here, I cannot refrain from mentioning that, when Pierre-Louis Lions obtained the Fields medal (1994), the commenda tion quoted explicitly his work with the late Ronald DiPerna on the existence of solutions of the Boltzmann equation.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 204 pp. Englisch. Nº de ref. del artículo: 9783764359850
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 exis tence 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 meth ods will be dealt with in some detail. Here, I cannot refrain from mentioning that, when Pierre-Louis Lions obtained the Fields medal (1994), the commenda tion quoted explicitly his work with the late Ronald DiPerna on the existence of solutions of the Boltzmann equation. 194 pp. Englisch. Nº de ref. del artículo: 9783764359850
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Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 exis tence 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 meth ods will be dealt with in some detail. Here, I cannot refrain from mentioning that, when Pierre-Louis Lions obtained the Fields medal (1994), the commenda tion quoted explicitly his work with the late Ronald DiPerna on the existence of solutions of the Boltzmann equation. Nº de ref. del artículo: 9783764359850
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