The Dirichlet problem for multidimensional hyperbola-parabolic equations with degeneracy of type and order
DOI:
https://doi.org/10.26577/jmmcs-2018-2-405Keywords:
multidimensional hyperbolic-parabolic equations, degeneration of type and porch, cylindrical domain, Dirichlet problem, solvability, Bessel functionAbstract
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
References
[2] Aldashev S.A. Zadacha Dirihle dlya vyrozhdayushchihsya mnogomernyh giperbolo-parabolicheskih uravnenij[ "The Dirichlet problem for degenerate multidimensional hyperbolic-parabolic equations,"] Scientific Bulletins of BelGU.mathematics, physics.no 45(2016):16-25.
[3] Aldashev S.A. Zadachi Darbu-Prottera dlya vyrozhdayushchihsya mnogomernyh giperbolicheskih uravnenij//Izvestiya vuzov, matematika["Darboux-Protter problems for degenerate multidimensional hyperbolic equations,"]. Proceedings of high schools,mathematics. no 9(532)(2006):3-9.
[4] Aldashev S.A. Vyrozhdayushchiesya mnogomernye giperbolicheskie uravneniya["Degenerating multidimensional hyperbolic equations"], Oral: ZKATU.(2007):139.
[5] Bateman G., Erdei A. Vysshie transcendentnye funkcii[Higher transcendental functions], vol.2(Moscow: Science,1974),297.
[6] Vragov V.N. Kraevye zadachi dlya neklassicheskih uravnenij matematicheskoj fiziki[Boundary value problems for nonclassical equations of mathematical physics],(NGU:1983),84.
[7] Kamke E. Spravochnik po obyknovennym differencial’nym uravneniyam[A Handbook of Ordinary Differential Equations] (Мoscow: Science,1965),703.
[8] Kolmogorov A.N, Fomin S.V. Elementy teorii funkcij i funkcional’nogo analiza[Elements of the theory of functions and functional analysis](Moscow:Science,1976),543.
[9] Maikotov M.N.(2017). Zadacha Dirihle dlya mnogomernyh giperbolicheskih uravnenij s vyrozhdeniem tipa i poryadka["The Dirichlet problem for multidimensional hyperbolic equations with degeneration of type and order],"Almaty: Bulletin of KazNPU named after Abai,no 59(2017):105-109.
[10] Mikhlin S.G. Mnogomernye singulyarnye integraly i integral’nye uravneniya[Multidimensional singular integrals and integral equations] (Moscow: Fizmatgiz,1962),254.
[11] Nakhushev A.M. Zadachi so smeshcheniem dlya uravneniya v chastnyh proizvodnyh[Problems with displacement for a partial differential equation](Moscow: Science,2006),287.
[12] Tikhonov A.N, Samarskii A.A. Equations of mathematical physics[Equations of mathematical physics](Мoscow: Science, 1966),724.
[13] Akhtyamov A.M. Vyrozhdennye kraevye usloviya dlya differencial’nogo uravneniya tret’ego poryadka["Degenerate boundary conditions for a third-order differential equation,"] Moscow: Science(2018):427.
