Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation

Ilgar Gurbat oglu Mamedov

doi:doi:10.11648/j.acm.20130203.15

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Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation

Ilgar Gurbat oglu Mamedov

Published in Applied and Computational Mathematics (Volume 2, Issue 3)

Received: 24 June 2013 Published: 20 July 2013

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Abstract

In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a final-boundary problem with non-classical boundary conditions is considered, which requires no matching conditions. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller's equation , moisture transfer generalized equation, Manjeron equation, Boussinesq-Love equation and etc.). It is grounded that the final-boundary conditions in the classic and non-classic treatment are equivalent to each other, and such boundary conditions are demonstrated in geometric form. Even from geometric interpretation can see that the grounded non-classic treatment doesn't require any additional conditions of agreement type. Thus, namely in this paper, the non-classic problem with final-boundary conditions is grounded for a pseudoparabolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev anisotropic space WP(4,2)(G) .

Published in	Applied and Computational Mathematics (Volume 2, Issue 3)
DOI	10.11648/j.acm.20130203.15
Page(s)	96-99
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), 2013. Published by Science Publishing Group

Keywords

Final-Boundary Value Problem, Pseudoparabolic Equations, Equations with Discontinuous Coefficients

References

[1]	D.Colton, "Pseudoparabolic equations in one space variable", J. Different. equations, 1972, vol.12, No3, pp.559-565.
[2]	A.P.Soldatov, M.Kh.Shkhanukov, "Boundary value problems with A.A.Samarsky general nonlocal condition for higher order pseudoparabolic equations", Dokl. AN SSSR, 1987, vol.297, No 3. pp.547-552 .
[3]	A.M.Nakhushev, Equations of mathematical biology. M.: Visshaya Shkola, 1995, 301p.
[4]	S.S.Akhiev, "Fundamental solution to some local and non - local boundary value problems and their representations ", DAN SSSR, 1983, vol.271, No 2, pp.265-269.
[5]	V.I.Zhegalov, E.A.Utkina, "On a third order pseudoparabolic equation", Izv. Vuzov, Matem., 1999, No 10, pp.73-76.
[6]	I.G.Mamedov, " A fundamental solution to the Cauchy problem for a fourth- order pseudoparabolic equation",Computational Mathematics and Mathematical Physics, 2009, volume 49, Issue 1, pp 93-104.
[7]	I.G.Mamedov, "A non-classical formula for integration by parts related to Goursat problem for a pseudoparabolic equation", Vladikavkazsky Matematicheskiy Zhurnal ,2011, vol.13, No 4, pp.40-51.
[8]	I.G.Mamedov, "Goursat non - classic three dimensional problem for a hyperbolic equation with discontinuous coefficients", Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta, 2010, No 1 (20), pp. 209-213.
[9]	I.G.Mamedov, "Final-boundary value problem for a hyperbolic equation with multi triple characteristics", Functional analysis and its applications, Proc. of the International Conference devoted to the centenary of acad. Z.I.Khalilov,Baku,2011,pp.232-234.

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Ilgar Gurbat oglu Mamedov. (2013). Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation. Applied and Computational Mathematics, 2(3), 96-99. https://doi.org/10.11648/j.acm.20130203.15

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Ilgar Gurbat oglu Mamedov. Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation. Appl. Comput. Math. 2013, 2(3), 96-99. doi: 10.11648/j.acm.20130203.15

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AMA Style

Ilgar Gurbat oglu Mamedov. Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation. Appl Comput Math. 2013;2(3):96-99. doi: 10.11648/j.acm.20130203.15

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@article{10.11648/j.acm.20130203.15,
  author = {Ilgar Gurbat oglu Mamedov},
  title = {Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {3},
  pages = {96-99},
  doi = {10.11648/j.acm.20130203.15},
  url = {https://doi.org/10.11648/j.acm.20130203.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130203.15},
  abstract = {In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a final-boundary problem with non-classical boundary conditions is considered, which requires no matching conditions. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller's equation , moisture transfer generalized equation, Manjeron equation, Boussinesq-Love equation and etc.). It is grounded that the final-boundary conditions in the classic and non-classic treatment are equivalent to each other, and such boundary conditions are demonstrated in geometric form. Even from geometric interpretation can see that the grounded non-classic treatment doesn't require any additional conditions of agreement type. Thus, namely in this paper, the non-classic problem with final-boundary conditions is grounded for a pseudoparabolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev anisotropic space WP(4,2)(G)  .},
 year = {2013}
}

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TY  - JOUR
T1  - Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation
AU  - Ilgar Gurbat oglu Mamedov
Y1  - 2013/07/20
PY  - 2013
N1  - https://doi.org/10.11648/j.acm.20130203.15
DO  - 10.11648/j.acm.20130203.15
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JO  - Applied and Computational Mathematics
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PB  - Science Publishing Group
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AB  - In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a final-boundary problem with non-classical boundary conditions is considered, which requires no matching conditions. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller's equation , moisture transfer generalized equation, Manjeron equation, Boussinesq-Love equation and etc.). It is grounded that the final-boundary conditions in the classic and non-classic treatment are equivalent to each other, and such boundary conditions are demonstrated in geometric form. Even from geometric interpretation can see that the grounded non-classic treatment doesn't require any additional conditions of agreement type. Thus, namely in this paper, the non-classic problem with final-boundary conditions is grounded for a pseudoparabolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev anisotropic space WP(4,2)(G)  .
VL  - 2
IS  - 3
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Author Information

Ilgar Gurbat oglu Mamedov

Institute of Cybernetics Azerbaijan National Academy of Sciences, B. Vahabzade St.9, Baku city, AZ 1141, Azerbaijan Republic

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APA Style

Ilgar Gurbat oglu Mamedov. (2013). Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation. Applied and Computational Mathematics, 2(3), 96-99. https://doi.org/10.11648/j.acm.20130203.15

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ACS Style

Ilgar Gurbat oglu Mamedov. Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation. Appl. Comput. Math. 2013, 2(3), 96-99. doi: 10.11648/j.acm.20130203.15

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AMA Style

Ilgar Gurbat oglu Mamedov. Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation. Appl Comput Math. 2013;2(3):96-99. doi: 10.11648/j.acm.20130203.15

Copy | Download

@article{10.11648/j.acm.20130203.15,
  author = {Ilgar Gurbat oglu Mamedov},
  title = {Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {3},
  pages = {96-99},
  doi = {10.11648/j.acm.20130203.15},
  url = {https://doi.org/10.11648/j.acm.20130203.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130203.15},
  abstract = {In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a final-boundary problem with non-classical boundary conditions is considered, which requires no matching conditions. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller's equation , moisture transfer generalized equation, Manjeron equation, Boussinesq-Love equation and etc.). It is grounded that the final-boundary conditions in the classic and non-classic treatment are equivalent to each other, and such boundary conditions are demonstrated in geometric form. Even from geometric interpretation can see that the grounded non-classic treatment doesn't require any additional conditions of agreement type. Thus, namely in this paper, the non-classic problem with final-boundary conditions is grounded for a pseudoparabolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev anisotropic space WP(4,2)(G)  .},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation
AU  - Ilgar Gurbat oglu Mamedov
Y1  - 2013/07/20
PY  - 2013
N1  - https://doi.org/10.11648/j.acm.20130203.15
DO  - 10.11648/j.acm.20130203.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 96
EP  - 99
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20130203.15
AB  - In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a final-boundary problem with non-classical boundary conditions is considered, which requires no matching conditions. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller's equation , moisture transfer generalized equation, Manjeron equation, Boussinesq-Love equation and etc.). It is grounded that the final-boundary conditions in the classic and non-classic treatment are equivalent to each other, and such boundary conditions are demonstrated in geometric form. Even from geometric interpretation can see that the grounded non-classic treatment doesn't require any additional conditions of agreement type. Thus, namely in this paper, the non-classic problem with final-boundary conditions is grounded for a pseudoparabolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev anisotropic space WP(4,2)(G)  .
VL  - 2
IS  - 3
ER  -

Copy | Download