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

Mahammad A. Nurmammadov

doi:doi:10.11648/j.ijtam.20150101.12

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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

Mahammad A. Nurmammadov

Published in International Journal of Theoretical and Applied Mathematics (Volume 1, Issue 1)

Received: 21 June 2015 Accepted: 30 June 2015 Published: 1 July 2015

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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.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 1, Issue 1)
DOI	10.11648/j.ijtam.20150101.12
Page(s)	10-20
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

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

References

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[6]	Canic S. B. L.Keyfitlz. A smooth solution for a Keldysh type equation. Comm. Partial Differential Equations , 21 (1-2) pp. 319-340,1996
[7]	Gui-Qiuang Chen and Mikhail Feldman. Multidimensional transonic shocks and free boundary value problems for nonlinear equation of mixed type . Journal American Math. Soc. 16 (2003) , 461-494
[8]	Fichera G. On a unified theory of boundary value problems for elliptic –parabolic equations of second order. Madison :The University of Wisconsin Press,pp.97-120,MR 0111931
[9]	Ladjenskaya O.A. The boundary value problems of mathematical physics .Applied Mathematical Sciences 49, Springer-Verlag ,New York, 1985
[10]	Lions, J.-L.Quelques methodes de resolution des problemas aux limites nolineaires, Paris, 1960
[11]	Morawetz C .S.,” A weak solution for a system of equations of elliptic-hyperbolic type,” Comm. Pure Appl. Math. Vol.11, pp. 315–331, 1958
[12]	Otway T.H. The Direchlet Problem For Elliptic-Hyperbolic Equations of Keldysh Type, Lecture Notes in Mathematics ISSN edition: 0075-8434, Springer Heidelberg Dordrecht, London, New York, 2012.
[13]	Lupo, D; Payne, K. R. Critical exponents for semi linear equations of mixed elliptic-hyperbolic and degenerate types. Comm. Pure Appl. Math. 56 (2003), no. 3, 403–424.
[14]	Pyatkov S,G. “On the solvability one boundary value problem for a forward-backward equation parabolic type”, Dokl. Akad Nauk SSSR, no.6, pp.1322-1327, 1985.
[15]	Sobolev S.L, Applications of Functional Analysis in Mathematical Physics, Izdat. Leningrad. Gos. Univ., Leningrad, 1950; English transl. Amer. Math. Soc, Providence, R.I., 1963.
[16]	Shuxing Chen. A nonlinear Lavrentev-Bistatze mixed type equation. Acta Mathematics Sciatic V. 31 Issues 6, 2011 p. 2378-2388.
[17]	Saracen L., On weak and strong solutions of boundary value problems, Comm. Pure Appl. Math. 15 (1962), 237-288. MR27 #460.
[18]	Tersenov S.A. About a forward-backward equation of parabolic type. Novosibirsk, Nauka, 1985
[19]	Nurmammadov M.A. On the solvability of the first local boundary value problems for linear systems equations of non-classical type with second order. Russian Academy of Sciences , Journal Doklad (Adigey) International Academy, Nalchik, 2008, v.10, №2, p.51-58 (in English)
[20]	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 , USA (in English)
[21]	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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Mahammad A. Nurmammadov. (2015). 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, 1(1), 10-20. https://doi.org/10.11648/j.ijtam.20150101.12

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ACS Style

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. Int. J. Theor. Appl. Math. 2015, 1(1), 10-20. doi: 10.11648/j.ijtam.20150101.12

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AMA Style

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. Int J Theor Appl Math. 2015;1(1):10-20. doi: 10.11648/j.ijtam.20150101.12

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@article{10.11648/j.ijtam.20150101.12,
  author = {Mahammad A. Nurmammadov},
  title = {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},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {1},
  number = {1},
  pages = {10-20},
  doi = {10.11648/j.ijtam.20150101.12},
  url = {https://doi.org/10.11648/j.ijtam.20150101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20150101.12},
  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.},
 year = {2015}
}

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TY  - JOUR
T1  - 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
AU  - Mahammad A. Nurmammadov
Y1  - 2015/07/01
PY  - 2015
N1  - https://doi.org/10.11648/j.ijtam.20150101.12
DO  - 10.11648/j.ijtam.20150101.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 10
EP  - 20
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20150101.12
AB  - 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.
VL  - 1
IS  - 1
ER  -

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Author Information

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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Mahammad A. Nurmammadov. (2015). 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, 1(1), 10-20. https://doi.org/10.11648/j.ijtam.20150101.12

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ACS Style

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. Int. J. Theor. Appl. Math. 2015, 1(1), 10-20. doi: 10.11648/j.ijtam.20150101.12

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AMA Style

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. Int J Theor Appl Math. 2015;1(1):10-20. doi: 10.11648/j.ijtam.20150101.12

Copy | Download

@article{10.11648/j.ijtam.20150101.12,
  author = {Mahammad A. Nurmammadov},
  title = {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},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {1},
  number = {1},
  pages = {10-20},
  doi = {10.11648/j.ijtam.20150101.12},
  url = {https://doi.org/10.11648/j.ijtam.20150101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20150101.12},
  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.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - 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
AU  - Mahammad A. Nurmammadov
Y1  - 2015/07/01
PY  - 2015
N1  - https://doi.org/10.11648/j.ijtam.20150101.12
DO  - 10.11648/j.ijtam.20150101.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 10
EP  - 20
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20150101.12
AB  - 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.
VL  - 1
IS  - 1
ER  -

Copy | Download