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Boundary Value Problems in Abstract Kinetic Theory

  • William Greenberg
  • Cornelis van der Mee
  • Vladimir Protopopescu

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

Table of contents

  1. Front Matter
    Pages i-x
  2. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 1-22
  3. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 23-54
  4. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 55-84
  5. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 85-107
  6. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 108-137
  7. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 138-160
  8. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 161-205
  9. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 206-241
  10. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 242-330
  11. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 331-364
  12. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 365-403
  13. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 404-439
  14. William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
    Pages 440-479
  15. Back Matter
    Pages 480-525

About this book

Introduction

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.

Keywords

Area biology Boundary value problem chemistry distribution equation Equivalence framework function functional analysis group theory Mathematica operator presentation stability

Authors and affiliations

  • William Greenberg
    • 1
  • Cornelis van der Mee
    • 2
  • Vladimir Protopopescu
    • 3
  1. 1.Virginia Polytechnic Institute & State UniversityBlacksburgUSA
  2. 2.Department of Mathematics & Computer ScienceClarkson UniversityPotsdamUSA
  3. 3.Engineering Physics & Mathematics DivisionOak Ridge National LaboratoryOak RidgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-5478-8
  • Copyright Information Birkhäuser Basel 1987
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-5480-1
  • Online ISBN 978-3-0348-5478-8
  • Series Print ISSN 0255-0156
  • Series Online ISSN 2296-4878
  • Buy this book on publisher's site