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
International Journal of Theoretical and Applied Mathematics
Volume 1, Issue 1, June 2015, Pages: 1-9
Received: Jun. 5, 2015;
Accepted: Jun. 16, 2015;
Published: Jun. 17, 2015
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Mahammad A. Nurmammadov, Department of Natural Sciences and its Teaching Methods of Azerbaijan Teachers Institute (Brunch Guba), Azerbaijan, Baku; Department of Mathematics and Department of Psychology of Khazar University, Azerbaijan, Baku
The solvability of the boundary value problem for linear systems of the mixed hyperbolic-elliptic equations of Keldysh type in the multivariate domain with the changing time direction are studied. Applying methods of functional analysis, “ -regularizing”, continuation by the parameter and by means of prior estimates, the existence and uniqueness of generalized and regular solutions of a boundary value problem are established in a weighted Sobolev space.
Mahammad A. Nurmammadov,
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, International Journal of Theoretical and Applied Mathematics.
Vol. 1, No. 1,
2015, pp. 1-9.
L. Sarason, On weak and strong solutions of boundary value problems, Comm. PureAppl. Math. 15 (1962), 237-288. MR27 #460.
Adams R. Sobolev Spaces, Second Ed., Academic Press, Elsevier Science, 2003.
A.V. Bitsadze, Some Classes of Partial Differential Equations, Gordon and Breach: New York, 1988.
V.N. Vragov, Boundary Value Problems for the Nonclassical Equations of Mathematical Physics, Novosibirsk: NSU, 1983. (in Russian).
S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics; English transl. Amer. Math. Soc, Providence, R.I., 1963.
L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Surveys in Applied Mathematics, vol. 3, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958.
F. I. Frankl, Selected Works in Gas Dynamics, Nauka, Moscow, Russia, 1973.
G. Fichera,“On a unified theory of boundary value problems for elliptic-parabolic equations of second order, ”Boundary Problems in Differential Equations, Univ. of Wisconsin Press, Madison, pp. 97–120, 1960.
Friedrichs, K. O. Symmetric positive linear differential equations. Comm. Pure Appl. Math. 11 (1958), 338–418.
Friedrichs, K. O. The identity of weak and strong differential operators. Trans. Amer. Math. Soc. 55 (1944), 132–151.
S. Canic, B. L. Keyfitz, E. H. Kim, “Mixed hyperbolic-elliptic system in self-similar flows,” Bol. Soc. Brasil. Mat.(N.S.) vol. 32, no. 3, pp. 377–399, 2001.
C. Somigliana. “Sui sisteme simmetrici di equazioni a derivate parziali,” Ann. Math. Pure et Appl., II, v. 22, pp.143-156, 1894.
B. Pini, Un Problem Di Valoru ol Contorno Por un’equazional a Derivative Puzziali Def Terro Ardine Con Parto Principale Di Tipo Composite, Rend. Sem. Fas. Sci. Univ. Gagliaro, 27, 114, 1957.
M.V. Keldysh, “ On certain classes of elliptic equations with singularity on the boundary of the domain, ,” Dokl. Akad. Nauk SSSR, 77, pp. 181–183, 1951.
O.A.Ladyzhenskaya, (English translation: The Boundary Value Problems of Mathematical Physic, Applied Mathematical Sciences, 49. Springer- Verlag, New York, 1985).
Tersenov S.A. About a forward-backward equation of parabolic type. Novosibirsk, Nauka, 1985 (in Russian) .
T.H. Otway, The Direchlet Problem For Elliptic-Hyperbolic Equations of Keldysh Type, Lecture Notes in Mathematics ISSN print edition:0075-8434, Springer Heidelberg Dordecht, London, New York, 2012.
D. Lupo, C.S. Morawetz, K.K. Peyne, “On closed boundary value problems for equations of elliptic-hyperbolic type”, Commun. Pure. Appl. Math., vol. 60, pp.1319-1348, 2007.
La’kin N.A, Novikov V.A.and Yonenko N.N. Nonlinear equations of variable type. Novosibirsk, 1983, Nauka.
C. S. Morawetz,” A weak solution for a system of equations of elliptic-hyperbolic type,” Comm. Pure Appl. Math. Vol.11, pp. 315–331, 1958
Nurmamedov M.A. On the solvability of the first local boundary value problems for linear systems equations of non-classical type with second order . Journal Doklad (Adigey) International Academy, Nalchik, 2008, v.10, №2, p.51-58 (in English)
Nurmammadov M.A. The Existence and Uniqueness of a New Boundary Value Problem (Type of Problem ‘‘E’’) for Linear System Equations of the Mixed Hyperbolic-Elliptic Type in the Multivariate Dimension with the Changing Time Direction. Hindavi Publishing Cooperation, Abstract and Applied Analysis Volume 2015, Research Article ID 7036552 pp. 1-10 (in English)