The Cauchy Problem In Kinetic Theory
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The Cauchy Problem In Kinetic Theory
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Author : Robert T. Glassey
language : en
Publisher: SIAM
Release Date : 1996-01-01
The Cauchy Problem In Kinetic Theory written by Robert T. Glassey and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Science categories.
Studies the basic equations of kinetic theory in all of space, and contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations. This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although describing very different phenomena, these equations share the same streaming term.
Mathematical Topics In Nonlinear Kinetic Theory
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Author : Nicola Bellomo
language : en
Publisher: World Scientific
Release Date : 1989-01-01
Mathematical Topics In Nonlinear Kinetic Theory written by Nicola Bellomo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.
This book has the aim of dealing with the Nonlinear evolution problems related to the spatially dependent Boltzmann and Enskog equations.
Singularly Perturbed Evolution Equations With Applications To Kinetic Theory
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Author : J. R. Mika
language : en
Publisher: World Scientific
Release Date : 1995
Singularly Perturbed Evolution Equations With Applications To Kinetic Theory written by J. R. Mika and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
In recent years there appeared a large number of papers as well as chapters in more general monographs devoted to evolution equations containing small (or large) parameters. In this book it is intended to gather the existing results as well as to introduce new ones on the field of initial value problems for singularly perturbed evolution equations of the resonance type. Such equations are of great interest in the applied sciences, particularly in the kinetic theory which is chosen as the main field of application for the asymptotic theory developed in the monograph.
Generalized Kinetic Models In Applied Sciences
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Author : Luisa Arlotti
language : en
Publisher: World Scientific
Release Date : 2003
Generalized Kinetic Models In Applied Sciences written by Luisa Arlotti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book deals with analytic problems related to some developments and generalizations of the Boltzmann equation toward the modeling and qualitative analysis of large systems that are of interest in applied sciences. These generalizations are documented in the various surveys edited by Bellomo and Pulvirenti with reference to models of granular media, traffic flow, mathematical biology, communication networks, and coagulation models. The first generalization dealt with refers to the averaged Boltzmann equation, which is obtained by suitable averaging of the distribution function of the field particles into the action domain of the test particle. This model is further developed to describe equations with dissipative collisions and a class of models that are of interest in mathematical biology. In this latter case the state of the particles is defined not only by a mechanical variable but also by a biological microscopic state.
Mathematical Topics In Nonlinear Kinetic Theory Ii
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Author : N. Bellomo
language : en
Publisher: World Scientific
Release Date : 1991
Mathematical Topics In Nonlinear Kinetic Theory Ii written by N. Bellomo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Science categories.
This book deals with the relevant mathematical aspects related to the kinetic equations for moderately dense gases with particular attention to the Enskog equation.
Advances In Kinetic Theory And Continuum Mechanics
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Author : Renee Gatignol
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Advances In Kinetic Theory And Continuum Mechanics written by Renee Gatignol and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
This volume contains the proceedings of the symposium held on Friday 6 July 1990 at the University Pierre et Marie Curie (Paris VI), France, in honor of Professor Henri Cabannes on the occasion of his retirement. There were about one hundred participants from nine countries: Canada, France, Germany, Italy, Japan, Norway, Portugal, the Netherlands, and the USA. Many of his past students or his colleagues were among the participants. The twenty-six papers in this volume are written versions submitted by the authors and cover almost all the fields in which Professor Cabannes has actively worked for more than forty-five years. The papers are presented in four chapters: classical kinetic theory and fluid dynamics, discrete kinetic theory, applied fluid mechanics, and continuum mechanics. The editors would like to take this opportunity to thank the generous spon sors of the symposium: the University Pierre et Marie Curie, Commissariat a l'Energie Atomique (especially Academician R. Dautray and Dr. N. Camarcat) and Direction des Recherches et Etudes Techniques (especially Professor P. Lallemand). Many thanks are also due to all the participants for making the symposium a success. Finally, we thank Professor W. Beiglbock and his team at Springer-Verlag for producing this volume.
Kinetic Boltzmann Vlasov And Related Equations
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Author : Alexander Sinitsyn
language : en
Publisher: Elsevier
Release Date : 2011-06-17
Kinetic Boltzmann Vlasov And Related Equations written by Alexander Sinitsyn and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-17 with Mathematics categories.
Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory. This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance. Reviews the whole field from the beginning to today Includes practical applications Provides classical and modern (semi-analytical) solutions
Many Particle Dynamics And Kinetic Equations
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Author : C. Cercignani
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Many Particle Dynamics And Kinetic Equations written by C. Cercignani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
As our title suggests, there are two aspects in the subject of this book. The first is the mathematical investigation of the dynamics of infinite systems of in teracting particles and the description of the time evolution of their states. The second is the rigorous derivation of kinetic equations starting from the results of the aforementioned investigation. As is well known, statistical mechanics started in the last century with some papers written by Maxwell and Boltzmann. Although some of their statements seemed statistically obvious, we must prove that they do not contradict what me chanics predicts. In some cases, in particular for equilibrium states, it turns out that mechanics easily provides the required justification. However things are not so easy, if we take a step forward and consider a gas is not in equilibrium, as is, e.g., the case for air around a flying vehicle. Questions of this kind have been asked since the dawn of the kinetic theory of gases, especially when certain results appeared to lead to paradoxical conclu sions. Today this matter is rather well understood and a rigorous kinetic theory is emerging. The importance of these developments stems not only from the need of providing a careful foundation of such a basic physical theory, but also to exhibit a prototype of a mathematical construct central to the theory of non-equilibrium phenomena of macroscopic size.
Kinetic Theories And The Boltzmann Equation
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Author : C. Cercignani
language : en
Publisher: Springer
Release Date : 2006-11-14
Kinetic Theories And The Boltzmann Equation written by C. Cercignani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Science categories.
Lecture Notes On The Mathematical Theory Of The Boltzmann Equation
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Author : N. Bellomo
language : en
Publisher: World Scientific
Release Date : 1995
Lecture Notes On The Mathematical Theory Of The Boltzmann Equation written by N. Bellomo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
This is a collection of four lectures on some mathematical aspects related to the nonlinear Boltzmann equation. The following topics are dealt with: derivation of kinetic equations, qualitative analysis of the initial value problem, singular perturbation analysis towards the hydrodynamic limit and computational methods towards the solution of problems in fluid dynamics.