The Cauchy problem in kinetic theory / Robert T. Glassey.

Format:

Book

Author/Creator:

Glassey, Robert, 1946-

Contributor:

Society for Industrial and Applied Mathematics.

Language:

English

Subjects (All):

Kinetic theory of matter--Mathematics.

Kinetic theory of matter.

Cauchy problem--Numerical solutions.

Cauchy problem.

Transport theory--Mathematics.

Transport theory.

Mathematical physics.

Physical Description:

1 online resource (xii, 241 p. ) ill. ;

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1996.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

This volume studies the basic equations of kinetic theory in all of space. It contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations, including the Boltzmann equation (from rarefied gas dynamics) and the Vlasov-Poisson/Vlasov-Maxwell systems (from plasma physics). This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although these equations describe very different phenomena, they share the same streaming term. The author proves that solutions starting from a given configuration at an initial time exist for all future times by imposing appropriate hypotheses on the initial values in several important cases. He emphasizes those questions that a mathematician would ask first: Is there a solution to this problem? Is it unique? Can it be numerically approximated? The topics treated include the study of the Boltzmann collision operator, the study of the initial-value problem for the Boltzmann equation with "small" and "near equilibrium" data, global smooth solvability of the initial-value problem for the Vlasov-Poisson system with smooth initial data of unrestricted size, conditions under which the initial-value problem for the Vlasov-Maxwell system has global-in-time solutions (in both the smooth and weak senses), and more.

Contents:

Preface

Chapter 1. Properties of the collision operator

Chapter 2. The Boltzmann equation near the vacuum

Chapter 3. The Boltzmann equation near the equilibrium

Chapter 4. The Vlasov

Poisson system

Chapter 5. The Vlasov

Maxwell system

Chapter 6. Dilute collisionless plasmas

Chapter 7. Velocity averages. weak solutions to the Vlasov

Chapter 8. Convergence of a particle method for the Vlasov

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Title from title screen, viewed 04/05/2011.

ISBN:

1-61197-147-0

Publisher Number:

OT52 SIAM