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Boundary Value Problems for Transport Equations

  • Valeri Agoshkov

Table of contents

About this book

Introduction

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].

Keywords

Boundary value algorithms calculus equation function geometry transport equations

Authors and affiliations

  • Valeri Agoshkov
    • 1
  1. 1.Russian Academy of SciencesInstitute of Numerical MathematicsMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1994-1
  • Copyright Information Birkhäuser Boston 1998
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7372-1
  • Online ISBN 978-1-4612-1994-1
  • Series Print ISSN 2164-3679
  • Buy this book on publisher's site
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