The Dirichlet problem for multidimensional hyperbola-parabolic equations with degeneracy of type and order

Abstract

The fundamental problems of mathematical physics-the study of the behavior of an oscillating
string-is incorrect when the boundary conditions are given on the entire boundary of the region.
As A. Bitsadze, A.Nakhushev noted, the Dirichlet problem is ill-posed (in the sense of unique
solvability) not only for the wave equation, but also for general hyperbolic equations. S.A Aldashev
previously studied the Dirichlet problem for degenerate multidimensional hyperbolic equations,
where a unique solvability of this problem is proved, which depends essentially on the height of
the cylindrical region under consideration. This paper shows the solvability of the Dirichlet problem
in a cylindrical domain for multidimensional hyperbola-parabolic equations with degeneration of
type and order.
Key words: multidimensional