CORRECTNESS OF THE MIXED PROBLEM FOR ONE CLASS OF DEGENERATE MULTIDIMENSIONAL HYPERBOLO-PARABOLIC EQUATIONS
Ключевые слова:
mixed problem, classical solution, unique solvability, Bessel functions, spherical functions.Аннотация
It is known that in mathematical modeling of electromagnetic fields in space, the nature of the
electromagnetic process is determined by the properties of the medium. If the medium is non-conductive, we get
degenerate multi-dimensional hyperbolic equations. If the medium has a high conductivity, then we go to degenerate
multidimensional parabolic equations.
Consequently, the analysis of electromagnetic fields in complex media (for example, if the conductivity of the
medium changes) reduces to degenerate multidimensional hyperbolic-parabolic equations.
Also, it is known that the oscillations of elastic membranes in space according to the Hamilton principle can be
modeled by degenerating multidimensional hyperbolic equations.
Studying the process of heat propagation in a medium filled with mass leads to degenerate multidimensional
parabolic equations.
Consequently, by studying the mathematical modeling of the process of heat propagation in oscillating elastic
membranes, we also come to degenerate multidimensional hyperbolic-parabolic equations. When studying these
applications, it is necessary to obtain an explicit representation of the solutions of the studied problems.
The mixed problem for degenerate multidimensional hyperbolic equations was previously considered.
As far as is known, these questions for degenerate multidimensional hyperbolic-parabolic equations have not
been studied.
In this paper, unique solvability is shown and an explicit form of the classical solution of the mixed problem for
one class of degenerate multidimensional hyperbolic-parabolic equations is obtained.
