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

  • M. N. Maikotov Kazakh national pedagogical university after Abay, Almaty, Kazakhstan

Abstract

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

References

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Published
2018-08-29
How to Cite
MAIKOTOV, M. N.. The Dirichlet problem for multidimensional hyperbola-parabolic equations with degeneracy of type and order. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 98, n. 2, p. 23-32, aug. 2018. ISSN 1563-0277. Available at: <http://bm.kaznu.kz/index.php/kaznu/article/view/405>. Date accessed: 10 dec. 2018. doi: https://doi.org/10.26577/jmmcs-2018-2-405.
Keywords multidimensional hyperbolic-parabolic equations, degeneration of type and porch, cylindrical domain, Dirichlet problem, solvability, Bessel function