The Solvability of a New Boundary Value Problem with Derivatives on the Boundary Conditions for Forward-Backward Semi Linear Systems Mixed of Keldysh Type in Multivariate Dimension
International Journal of Theoretical and Applied Mathematics
Volume 1, Issue 1, June 2015, Pages: 10-20
Received: Jun. 21, 2015; Accepted: Jun. 30, 2015; Published: Jul. 1, 2015
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Author
Mahammad A. Nurmammadov, Department of Natural Sciences and its Teaching Methods (Guba Branch) of Azerbaijan Teachers Institute, Baku, Azerbaijan; Department of Mathematics and Department of Psychology of the Khazar University, Baku, Azerbaijan
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Abstract
Abstract. In present paper we investigate solvability of a new boundary value problem with derivatives on the boundary conditions for semi-linear systems of mixed hyperbolic-elliptic of Keldysh type equations in multivariate dimension with the changing time direction . Considered problem and system equations are new and belong to modern level of partial differential equations, moreover contain partition degenerating elliptic, degenerating hyperbolic, mixed and composite type differential equations. Applying methods of functional analysis, topological methods, “ -regularizing» and continuation by the parameter at the same time with aid of a prior estimates, under assumptions conditions on coefficients of equations of system, the existence and uniqueness of generalized and regular solutions of a boundary value problem are established in a weighted Sobolev’s space. In this work one of main idea, the identity of strong and weak solution is established.
Keywords
Changing Time Direction, Weighted Sobolev’s Space, Equation of Mixed Type, Strong, Weak and Regular Solution, Forward-Backward Equations, System Equations of Mixed Hyperbolic-Elliptic Keldysh Type
To cite this article
Mahammad A. Nurmammadov, The Solvability of a New Boundary Value Problem with Derivatives on the Boundary Conditions for Forward-Backward Semi Linear Systems Mixed of Keldysh Type in Multivariate Dimension, International Journal of Theoretical and Applied Mathematics. Vol. 1, No. 1, 2015, pp. 10-20. doi: 10.11648/j.ijtam.20150101.12
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Nurmammadov M. A. The Solvability of a New Boundary Value Problem with Derivatives on the Boundary Conditions for Forward-Backward Linear Systems Mixed of Keldysh Type in Multivariate Dimension. Sciences Publishing Group, International Journal of Theoretical and Applied Mathematics. Vol.1, No1, 2015 pp. 1-9. doi: 10.11648/j.ijtam.20150101.11 New York, USA (in English)
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