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]."
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