Overview
- Authors:
-
-
William Greenberg
-
Virginia Polytechnic Institute & State University, Blacksburg, USA
-
Cornelis Mee
-
Department of Mathematics & Computer Science, Clarkson University, Potsdam, USA
-
Vladimir Protopopescu
-
Engineering Physics & Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, USA
Access this book
Other ways to access
Table of contents (13 chapters)
-
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 1-22
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 23-54
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 55-84
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 85-107
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 108-137
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 138-160
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 161-205
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 206-241
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 242-330
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 331-364
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 365-403
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 404-439
-
- William Greenberg, Cornelis van der Mee, Vladimir Protopopescu
Pages 440-479
-
Back Matter
Pages 480-525
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