Dirichlet problem for three-dimensional hyperbolic-parabolic equations with type and order extinction
Keywords:
Dirichlet problem, degeneration of the type and order, solvability, densityAbstract
Boundary value problems for hyperbolic-parabolic equations in the plane have been studied
properly, where Tricomi problem and the first boundary value problem were investigated.
The mixed problem, Cauchy characteristic problem and Darboux problem for multidimensional
hyperbolic-parabolic equations have been considered before. Different authors have defined and
investigated Tricomi problem for hyperbolic-parabolic equations in multidimensional domains. The
theory of boundary value problems for degenerating hyperbolic-parabolic equations in the plane has
also been studied properly. Besides, multidimensional analogues of these problems in generalized
spaces have been investigated. Correctness of Dirichlet problems for degenerating multidimensional
hyperbolic equations has been proved. In this work the author showed solvability and obtained
an explicit classical solution of Dirichlet problem in a cylindrical domain for three-dimensional
hyperbolic-parabolic equations with type and order extinction.
References
[2] Vragov V.N. Boundary value problems for nonclassical equations of Math Physics. -Novosibirsk: NSU, 1983.- 84 p.
[3] Aldashev S. A. Correctness of Dirichlet and Poincare problem in a cylindrical domain for degenerating multi-dimensional hyperbolic equations with Chaplygin operator // НScientific gazette of BelSU. «Mathematics, Physics». -Belgorod: 2012, - Vol. 26, No. 5(124). – P. 12-25.
[4] Aldashev S. A. DirichletandPoincareproblemsinacylindricaldomainfordegeneratingthree-dimensionalhyperbolicequations // Mater. of IV internation. conf. «Math Physics and its applications». – Samara: SamSU, 2014. – P. 46.
[5] Kolmogorov A. N., Fomin S. V. Elements of function theory and functional analysis. –M.: Nauka, 1976, - P. 543.
[6] Aldashev S. A. Correctness of Dirichlet problem for degenerating multi-dimensional hyperbolic-parabolic equations// Vladicaucasusmath journal. -2014. -vol. 16, No.4 . P. 3-8.
[7] Kitaybekov. E.T. Dirichlet problem in a cylindrical domain for three-dimensional hyperbolic equations with type and order confluence // Bulletin of KazNPU named after. Abay. Series of physical-math sciences. –Almaty. 2015. No. 4(52). – P. 27-31.
