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Boundary Value Problems for Transport Equations

  • Book
  • © 1998

Overview

Authors:
  1. Valeri Agoshkov

    1. Russian Academy of Sciences, Institute of Numerical Mathematics, Moscow, Russia

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Problems and equations of transport theory

    • Valeri Agoshkov
    Pages 1-34

  3. Functional spaces, existence of traces, and extension of functions

    • Valeri Agoshkov
    Pages 35-104

  4. Variational statements and generalized solutions of transport problems

    • Valeri Agoshkov
    Pages 105-163

  5. Regularity properties of generalized solutions

    • Valeri Agoshkov
    Pages 164-215

  6. Applications to analysis of transport problems and numerical algorithms

    • Valeri Agoshkov
    Pages 216-262

  7. Back Matter

    Pages 263-278
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Keywords

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].

Authors and Affiliations

  • Russian Academy of Sciences, Institute of Numerical Mathematics, Moscow, Russia

    Valeri Agoshkov

Bibliographic Information

  • Book Title: Boundary Value Problems for Transport Equations

  • Authors: Valeri Agoshkov

  • Series Title: Modeling and Simulation in Science, Engineering and Technology

  • DOI: https://doi.org/10.1007/978-1-4612-1994-1

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1998

  • Hardcover ISBN: 978-0-8176-3986-0Published: 29 September 1998

  • Softcover ISBN: 978-1-4612-7372-1Published: 23 October 2012

  • eBook ISBN: 978-1-4612-1994-1Published: 06 December 2012

  • Series ISSN: 2164-3679

  • Series E-ISSN: 2164-3725

  • Edition Number: 1

  • Number of Pages: XVII, 278

  • Topics: Analysis, Mathematics, general

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