The Dirichlet problem for multidimensional hyperbola-parabolic equations with degeneracy of type and order (Journal of Mathematics Mechanics and Computer Science, 2018)
The fundamental problems of mathematical physics-the study of the behavior of an oscillatingstring-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 uniquesolvability) not only for the wave equation, but also for general hyperbolic equations. S.A Aldashevpreviously studied the Dirichlet problem for degenerate multidimensional hyperbolic equations,where a unique solvability of this problem is proved, which depends essentially on the height ofthe cylindrical region under consideration. This paper shows the solvability of the Dirichlet problemin a cylindrical domain for multidimensional hyperbola-parabolic equations with degeneration oftype and order.Key words: multidimensional
Keywords: multidimensional hyperbolic-parabolic equations; degeneration of type and porch; cylindrical domain; Dirichlet problem; solvability; Bessel function