Kinetic Boltzmann, Vlasov and related equations

Medientyp: E-Book

Titel: Kinetic Boltzmann, Vlasov and related equations

Enthält: Front Cover; Kinetic Boltzmann, Vlasov and Related Equations; Copyright; Table of Contents; Preface; About the Authors; Chapter 1. Principal Concepts of Kinetic Equations; 1.1 Introduction; 1.2 Kinetic Equations of Boltzmann Kind; 1.3 Vlasov's Type Equations; 1.4 How did the Concept of Distribution Function Explain Molecular-Kinetic and Gas Laws to Maxwell; 1.5 On a Kinetic Approach to the Sixth Hilbert Problem (Axiomatization of Physics); 1.6 Conclusions; Chapter 2. Lagrangian Coordinates; 2.1 The Problem of N-Bodies, Continuum of Bodies, and Lagrangian Coordinates in Vlasov Equation
2.2 When the Equations for Continuum of Bodies Become Hamiltonian?2.3 Oscillatory Potential Example; 2.4 Antioscillatory Potential Example; 2.5 Hydrodynamical Substitution: Multiflow Hydrodynamics and Euler-Lagrange Description; 2.6 Expanding Universe Paradigm; 2.7 Conclusions; Chapter 3. Vlasov-Maxwell and Vlasov-Einstein Equations; 3.1 Introduction; 3.2 A Shift of Density Along the Trajectories of Dynamical System; 3.3 Geodesic Equations and Evolution of Distribution Function on Riemannian Manifold; 3.4 How does the Riemannian Space Measure Behave While Being Transformed?
3.5 Derivation of the Vlasov-Maxwell Equation3.6 Derivation Scheme of Vlasov-Einstein Equation; 3.7 Conclusion; Chapter 4. Energetic Substitution; 4.1 System of Vlasov-Poisson Equations for Plasma and Electrons; 4.2 Energetic Substitution and Bernoulli Integral; 4.3 Boundary-Value Problem for Nonlinear Elliptic Equation; 4.4 Verifying the Condition ?' = 0; 4.5 Conclusions; Chapter 5. Introduction to the Mathematical Theory of Kinetic Equations; 5.1 Characteristics of the System; 5.2 Vlasov-Maxwell and Vlasov-Poisson Systems; 5.3 Weak Solutions of Vlasov-Poisson and Vlasov-Maxwell Systems
5.4 Classical Solutions of VP and VM Systems5.5 Kinetic Equations Modeling Semiconductors; 5.6 Open Problems for Vlasov-Poisson and Vlasov-Maxwell Systems; Chapter 6. On the Family of the Steady-State Solutions of Vlasov-Maxwell System; 6.1 Ansatz of the Distribution Function and Reduction of Stationary Vlasov-Maxwell Equations to Elliptic System; 6.2 Boundary Value Problem; 6.3 Solutions with Norm; Chapter 7. Boundary Value Problems for the Vlasov-Maxwell System; 7.1 Introduction
7.2 Existence and Properties of the Solutions of the Vlasov-Maxwell and Vlasov-Poisson Systems in the Bounded Domains7.3 Existence and Properties of Solutions of the VM System in the Bounded Domains; 7.4 Collisionless Kinetic Models (Classical and Relativistic Vlasov-Maxwell Systems); 7.5 Stationary Solutions of Vlasov-Maxwell System; 7.6 Existence of Solutions for the Boundary Value Problem (7.5.28)-(7.5.30); 7.7 Existence of Solution for Nonlocal Boundary Value Problem; 7.8 Nonstationary Solutions of the Vlasov-Maxwell System
7.9 Linear Stability of the Stationary Solutions of the Vlasov-Maxwell System

Beteiligte: Vedenyapin, Victor [VerfasserIn]; Sinitsyn, Alexander [VerfasserIn]; Dulov, Eugene [VerfasserIn]

Erschienen: Amsterdam; Heidelberg [u.a.]: Elsevier, 2011
Online-Ausg.

Ausgabe: 1 ed.

Umfang: XIII, 304 S.; graf. Darst

Sprache: Englisch

ISBN: 9780123877796; 0123877792; 1283134055; 9781283134057

RVK-Notation: UF 1950 : Dynamik, Kinetik

Schlagwörter: Online-Ressource

Art der Reproduktion: Online-Ausg.

Entstehung:

Anmerkungen: Includes bibliographical references

Beschreibung: 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. <ul> <li>Reviews the whole field from the beginning to today</li> <li>Includes practical applications</li> <li>Provides classical and modern (semi-analytical) solutions</li></ul>

Kinetic Boltzmann, Vlasov and related equations - [1 ed.]

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