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Boundary Value Problems in Abstract Kinetic Theory

  • Book
  • © 1987

Overview

Authors:
  1. William Greenberg

    1. Virginia Polytechnic Institute & State University, Blacksburg, USA

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  2. Cornelis Mee

    1. Department of Mathematics & Computer Science, Clarkson University, Potsdam, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Vladimir Protopopescu

    1. Engineering Physics & Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, USA

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Part of the book series: Operator Theory: Advances and Applications (OT, volume 23)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Elements of Linear Kinetic Theory

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 1-22

  3. Strictly Dissipative Kinetic Models

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 23-54

  4. Conservative Kinetic Models

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 55-84

  5. Non-Dissipative and Non-Symmetric Kinetic Models

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 85-107

  6. Kinetic Equations on Finite Domains

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 108-137

  7. Equivalence of Differential and Integral Formulations

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 138-160

  8. Semigroup Factorization and Reconstruction

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 161-205

  9. Albedo Operators, H-Equations and Representation of Solutions

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 206-241

  10. Applications of the Stationary Theory

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 242-330

  11. Indefinite Sturm-Liouville Problems

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 331-364

  12. Time Dependent Kinetic Equations: Method of Characteristics

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 365-403

  13. Time Dependent Kinetic Equations: Semigroup Approach

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 404-439

  14. Applications of the Initial Value Problem

    • William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 440-479

  15. Back Matter

    Pages 480-525
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Keywords

About this book

This monograph is intended to be a reasonably self -contained and fairly complete exposition of rigorous results in abstract kinetic theory. Throughout, abstract kinetic equations refer to (an abstract formulation of) equations which describe transport of particles, momentum, energy, or, indeed, any transportable physical quantity. These include the equations of traditional (neutron) transport theory, radiative transfer, and rarefied gas dynamics, as well as a plethora of additional applications in various areas of physics, chemistry, biology and engineering. The mathematical problems addressed within the monograph deal with existence and uniqueness of solutions of initial-boundary value problems, as well as questions of positivity, continuity, growth, stability, explicit representation of solutions, and equivalence of various formulations of the transport equations under consideration. The reader is assumed to have a certain familiarity with elementary aspects of functional analysis, especially basic semigroup theory, and an effort is made to outline any more specialized topics as they are introduced. Over the past several years there has been substantial progress in developing an abstract mathematical framework for treating linear transport problems. The benefits of such an abstract theory are twofold: (i) a mathematically rigorous basis has been established for a variety of problems which were traditionally treated by somewhat heuristic distribution theory methods; and (ii) the results obtained are applicable to a great variety of disparate kinetic processes. Thus, numerous different systems of integrodifferential equations which model a variety of kinetic processes are themselves modelled by an abstract operator equation on a Hilbert (or Banach) space.

Authors and Affiliations

  • Virginia Polytechnic Institute & State University, Blacksburg, USA

    William Greenberg

  • Department of Mathematics & Computer Science, Clarkson University, Potsdam, USA

    Cornelis Mee

  • Engineering Physics & Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, USA

    Vladimir Protopopescu

Bibliographic Information

  • Book Title: Boundary Value Problems in Abstract Kinetic Theory

  • Authors: William Greenberg, Cornelis Mee, Vladimir Protopopescu

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-5478-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1987

  • Softcover ISBN: 978-3-0348-5480-1Published: 11 April 2014

  • eBook ISBN: 978-3-0348-5478-8Published: 14 December 2013

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: X, 525

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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