Boundary Value Problems for Transport Equations (Modeling and Simulation in Science, Engineering and Technology) - Hardcover

Agoshkov, Valeri

Hardcover

ISBN 10: 0817639861 ISBN 13: 9780817639860

Publisher: Birkhäuser, 1998

Synopsis

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].

About this title

Synopsis

This text develops a functional approach for boundary value problems and includes the following components; the introduction of special functional spaces; the definition of spaces for boundary values; the analysis of the problems of trace existence; and the extension of functions with preservation of classes of regularity. This approach proves the existence of generalized solutions to problems concerned on the basis of those functional spaces introduced and also proper variational formulations of problems. The book also presents various applications of the theory developed.

Edition details

• Publisher: Birkhäuser
• Publication date: 1998
• Language: English
• ISBN 10: 0817639861
• ISBN 13: 9780817639860
• Binding: Hardcover
• Number of pages: 278