Modeling and Simulation in Science, Engineering and Technology

Boundary Value Problems for Transport Equations

Authors: Agoshkov, Valeri

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About this book

In the modern theory of boundary value problems the following ap­ proach to investigation is agreed upon (we call it the functional approach): some functional spaces are chosen; the statements of boundary value prob­ the basis of these spaces; and the solvability of lems are formulated on the problems, properties of solutions, and their dependence on the original data of the problems are analyzed. These stages are put on the basis of the correct statement of different problems of mathematical physics (or of the definition of ill-posed problems). For example, if the solvability of a prob­ lem in the functional spaces chosen cannot be established then, probably, the reason is in their unsatisfactory choice. Then the analysis should be repeated employing other functional spaces. Elliptical problems can serve as an example of classical problems which are analyzed by this approach. Their investigations brought a number of new notions and results in the theory of Sobolev spaces W;(D) which, in turn, enabled us to create a sufficiently complete theory of solvability of elliptical equations. Nowadays the mathematical theory of radiative transfer problems and kinetic equations is an extensive area of modern mathematical physics. It has various applications in astrophysics, the theory of nuclear reactors, geophysics, the theory of chemical processes, semiconductor theory, fluid mechanics, etc. [25,29,31,39,40, 47, 52, 78, 83, 94, 98, 120, 124, 125, 135, 146].

Table of contents (5 chapters)

  • Problems and equations of transport theory

    Agoshkov, Valeri

    Pages 1-34

  • Functional spaces, existence of traces, and extension of functions

    Agoshkov, Valeri

    Pages 35-104

  • Variational statements and generalized solutions of transport problems

    Agoshkov, Valeri

    Pages 105-163

  • Regularity properties of generalized solutions

    Agoshkov, Valeri

    Pages 164-215

  • Applications to analysis of transport problems and numerical algorithms

    Agoshkov, Valeri

    Pages 216-262

Buy this book

eBook £55.99
price for United Kingdom (gross)
  • ISBN 978-1-4612-1994-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover £89.99
price for United Kingdom (gross)
  • ISBN 978-0-8176-3986-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover £69.99
price for United Kingdom (gross)
  • ISBN 978-1-4612-7372-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Boundary Value Problems for Transport Equations
Authors
Series Title
Modeling and Simulation in Science, Engineering and Technology
Copyright
1998
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-1-4612-1994-1
DOI
10.1007/978-1-4612-1994-1
Hardcover ISBN
978-0-8176-3986-0
Softcover ISBN
978-1-4612-7372-1
Series ISSN
2164-3679
Edition Number
1
Number of Pages
XVII, 278
Topics