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

Mahammad A. Nurmammadov

doi:doi:10.11648/j.ijtam.20150101.11

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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

Mahammad A. Nurmammadov

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

Received: 5 June 2015 Accepted: 16 June 2015 Published: 17 June 2015

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Abstract

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.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 1, Issue 1)
DOI	10.11648/j.ijtam.20150101.11
Page(s)	1-9
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), 2024. Published by Science Publishing Group

Keywords

Changing Time Direction, Weighted Sobolev Space, System Equations of Mixed Type, Weak, Strong and Regular Solution, Forward-Backward Linear Systems Mixed of Keldysh Type

References

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[12]	C. Somigliana. “Sui sisteme simmetrici di equazioni a derivate parziali,” Ann. Math. Pure et Appl., II, v. 22, pp.143-156, 1894.
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[14]	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.
[15]	O.A.Ladyzhenskaya, (English translation: The Boundary Value Problems of Mathematical Physic, Applied Mathematical Sciences, 49. Springer- Verlag, New York, 1985).
[16]	Tersenov S.A. About a forward-backward equation of parabolic type. Novosibirsk, Nauka, 1985 (in Russian) .
[17]	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.
[18]	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.
[19]	La’kin N.A, Novikov V.A.and Yonenko N.N. Nonlinear equations of variable type. Novosibirsk, 1983, Nauka.
[20]	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
[21]	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)
[22]	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)

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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 Linear Systems Mixed of Keldysh Type in Multivariate Dimension. International Journal of Theoretical and Applied Mathematics, 1(1), 1-9. https://doi.org/10.11648/j.ijtam.20150101.11

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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 Linear Systems Mixed of Keldysh Type in Multivariate Dimension. Int. J. Theor. Appl. Math. 2015, 1(1), 1-9. doi: 10.11648/j.ijtam.20150101.11

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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 Linear Systems Mixed of Keldysh Type in Multivariate Dimension. Int J Theor Appl Math. 2015;1(1):1-9. doi: 10.11648/j.ijtam.20150101.11

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@article{10.11648/j.ijtam.20150101.11,
  author = {Mahammad A. Nurmammadov},
  title = {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},
  journal = {International Journal of Theoretical and Applied Mathematics},
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  pages = {1-9},
  doi = {10.11648/j.ijtam.20150101.11},
  url = {https://doi.org/10.11648/j.ijtam.20150101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20150101.11},
  abstract = {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.},
 year = {2015}
}

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T1  - 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
AU  - Mahammad A. Nurmammadov
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Author Information

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

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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 Linear Systems Mixed of Keldysh Type in Multivariate Dimension. International Journal of Theoretical and Applied Mathematics, 1(1), 1-9. https://doi.org/10.11648/j.ijtam.20150101.11

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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 Linear Systems Mixed of Keldysh Type in Multivariate Dimension. Int. J. Theor. Appl. Math. 2015, 1(1), 1-9. doi: 10.11648/j.ijtam.20150101.11

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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 Linear Systems Mixed of Keldysh Type in Multivariate Dimension. Int J Theor Appl Math. 2015;1(1):1-9. doi: 10.11648/j.ijtam.20150101.11

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@article{10.11648/j.ijtam.20150101.11,
  author = {Mahammad A. Nurmammadov},
  title = {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},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {1},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.ijtam.20150101.11},
  url = {https://doi.org/10.11648/j.ijtam.20150101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20150101.11},
  abstract = {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.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - 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
AU  - Mahammad A. Nurmammadov
Y1  - 2015/06/17
PY  - 2015
N1  - https://doi.org/10.11648/j.ijtam.20150101.11
DO  - 10.11648/j.ijtam.20150101.11
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  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20150101.11
AB  - 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.
VL  - 1
IS  - 1
ER  -

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