Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain

Aliev Nehan Ali; Abbasova Aygun Khanlar; Zeynalov Ramin M.

doi:doi:10.11648/j.sjams.20130101.11

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Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain

Aliev Nehan Ali, Abbasova Aygun Khanlar, Zeynalov Ramin M.

Published in Science Journal of Applied Mathematics and Statistics (Volume 1, Issue 1)

Published: 2 April 2013

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Abstract

In classic mathematical physics course, under the local boundary conditions the Dirichlet (first kind), Neuman (second kind) and at last special case of Poincare (third kind) boundary value problems were considered for a Laplace equation being a canonic form of elliptic type of equations. Later on for a Laplace equation, under non-local boundary condition the Steklov problem was investigated in [3] and a sufficient condition for Fredholm property was found. Note that here boundary conditions contains non -local and global terms and the investigation method consist of obtaining necessary conditions, regularization of them and reducing the stated boundary problem to the system of second kind Fredholm integral equation with non-singular kernel.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 1, Issue 1)
DOI	10.11648/j.sjams.20130101.11
Page(s)	1-6
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

Boundary Value Problem, Local, Non-Local And Global Boundary Condition, Steklov Problem, Necessary Conditions, Regularization, Fredholm Property

References

[1]	Courant R., Partial Equations.,М., "Мir" publishing house, 1964, 830 рp.
[2]	Vladimirov V.S., Equations of mathematical physics. M., "Nauka" publishing house, 1981, 512 pр.
[3]	Aliev N.A., Suleymanov N. Investigation of solutions of boundary value problems containing a parameter in the boundary condition. Numerical methods to boundary value problems., (subject collection of scientific papers) Azerbaijan. University., Baku, 1989, p. 3-5.
[4]	Aliev N. and Jahanshahi M., Solution of Poisson’s equation with qlobal, local and non-local boundary conditions., International Journal of Mathematical Education in Science and Technology, vol 33 (2002), №2, pp.241-247.
[5]	Bahrami, F., Aliev, N., Hosseini,, S.M., A Method for the reduction of four dimensional mixed problems with general boundary conditions to a system of second kind Fredholm inteqral equations. Italian Journal of pure and applied Mathematics, №17 (January 2005), pp.91-104.
[6]	Aliev, N., Rezapour, Sh., Jahanshahi, M., A mixed problem for Navier-Stokes System, Mathematica Moravica Journal of University of Kragujevac, Serbia vol. 12-2 (2008), pp. 1-14.
[7]	Aliev N.A, Abbasova A.Kh., The new approach to boundary problems for Cauchy-Riemann equation., News of Baku University, Series of Physico-Mathematical sciences, Azerbaijan, Baku,Vol.2, 2010, pp. 49-53.
[8]	Abbasova A.Kh., Aliev N.A., About the Stefan problem for the Cauchy-Riemann equation with non-local and global terms in the boundary conditions., Material’s International conference on mathematical theories and problems of their application and teaching is dedicated to the 870-th anniversary of great poet and philosopher Nizami Ganjavi, Azerbaijan, Ganja, September 23-25, 2011,pp.45-48.
[9]	Abbasova A.Kh., Aliev N.A., Boundary problem on stripe with curvilinear boundaries., Journal of Contemporary Applied Mathematics, Vol.1, Issue 2, pp.67-71, December, 2011.
[10]	Aliev N.A., Zeynalov R.M., Steklov problem for a first order elliptic type of equation. / News of Baku University, Series of Physico-Mathematical sciences, Azerbaijan, Baku,Vol.2, 2012,pp.13-21..
[11]	Abbasova A.Kh., Aliev N.A., Solution of boundary value problem for Cauchy-Riemann equation in half-plane field./ Material’s of XIV International scientific Kravchuk conference , Ukraine, Kiev, April 19-21,2012, pp.40-43.

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Aliev Nehan Ali, Abbasova Aygun Khanlar, Zeynalov Ramin M. (2013). Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain. Science Journal of Applied Mathematics and Statistics, 1(1), 1-6. https://doi.org/10.11648/j.sjams.20130101.11

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ACS Style

Aliev Nehan Ali; Abbasova Aygun Khanlar; Zeynalov Ramin M. Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain. Sci. J. Appl. Math. Stat. 2013, 1(1), 1-6. doi: 10.11648/j.sjams.20130101.11

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AMA Style

Aliev Nehan Ali, Abbasova Aygun Khanlar, Zeynalov Ramin M. Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain. Sci J Appl Math Stat. 2013;1(1):1-6. doi: 10.11648/j.sjams.20130101.11

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@article{10.11648/j.sjams.20130101.11,
  author = {Aliev Nehan Ali and Abbasova Aygun Khanlar and Zeynalov Ramin M.},
  title = {Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {1},
  number = {1},
  pages = {1-6},
  doi = {10.11648/j.sjams.20130101.11},
  url = {https://doi.org/10.11648/j.sjams.20130101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20130101.11},
  abstract = {In classic mathematical physics course, under the local boundary conditions the Dirichlet (first kind), Neuman (second kind) and at last special case of Poincare (third kind) boundary value problems were considered for a Laplace equation being a canonic form of elliptic type of equations. Later on for a Laplace equation, under non-local boundary condition the Steklov problem was investigated in [3] and a sufficient condition for Fredholm property was found. Note that here boundary conditions contains non -local and global terms and the investigation method consist of obtaining necessary conditions, regularization of them and reducing the stated boundary problem to the system of second kind Fredholm integral equation with non-singular kernel.},
 year = {2013}
}

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TY  - JOUR
T1  - Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain
AU  - Aliev Nehan Ali
AU  - Abbasova Aygun Khanlar
AU  - Zeynalov Ramin M.
Y1  - 2013/04/02
PY  - 2013
N1  - https://doi.org/10.11648/j.sjams.20130101.11
DO  - 10.11648/j.sjams.20130101.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 1
EP  - 6
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20130101.11
AB  - In classic mathematical physics course, under the local boundary conditions the Dirichlet (first kind), Neuman (second kind) and at last special case of Poincare (third kind) boundary value problems were considered for a Laplace equation being a canonic form of elliptic type of equations. Later on for a Laplace equation, under non-local boundary condition the Steklov problem was investigated in [3] and a sufficient condition for Fredholm property was found. Note that here boundary conditions contains non -local and global terms and the investigation method consist of obtaining necessary conditions, regularization of them and reducing the stated boundary problem to the system of second kind Fredholm integral equation with non-singular kernel.
VL  - 1
IS  - 1
ER  -

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Author Information

Aliev Nehan Ali

Baku State University, Baku, Azerbaijan
Abbasova Aygun Khanlar

Baku State University, Baku, Azerbaijan
Zeynalov Ramin M.

Institute of Cybernetics of Azerbaijan National Academy of Sciences, Baku, Azerbaijan

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APA Style

Aliev Nehan Ali, Abbasova Aygun Khanlar, Zeynalov Ramin M. (2013). Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain. Science Journal of Applied Mathematics and Statistics, 1(1), 1-6. https://doi.org/10.11648/j.sjams.20130101.11

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ACS Style

Aliev Nehan Ali; Abbasova Aygun Khanlar; Zeynalov Ramin M. Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain. Sci. J. Appl. Math. Stat. 2013, 1(1), 1-6. doi: 10.11648/j.sjams.20130101.11

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AMA Style

Aliev Nehan Ali, Abbasova Aygun Khanlar, Zeynalov Ramin M. Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain. Sci J Appl Math Stat. 2013;1(1):1-6. doi: 10.11648/j.sjams.20130101.11

Copy | Download

@article{10.11648/j.sjams.20130101.11,
  author = {Aliev Nehan Ali and Abbasova Aygun Khanlar and Zeynalov Ramin M.},
  title = {Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {1},
  number = {1},
  pages = {1-6},
  doi = {10.11648/j.sjams.20130101.11},
  url = {https://doi.org/10.11648/j.sjams.20130101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20130101.11},
  abstract = {In classic mathematical physics course, under the local boundary conditions the Dirichlet (first kind), Neuman (second kind) and at last special case of Poincare (third kind) boundary value problems were considered for a Laplace equation being a canonic form of elliptic type of equations. Later on for a Laplace equation, under non-local boundary condition the Steklov problem was investigated in [3] and a sufficient condition for Fredholm property was found. Note that here boundary conditions contains non -local and global terms and the investigation method consist of obtaining necessary conditions, regularization of them and reducing the stated boundary problem to the system of second kind Fredholm integral equation with non-singular kernel.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain
AU  - Aliev Nehan Ali
AU  - Abbasova Aygun Khanlar
AU  - Zeynalov Ramin M.
Y1  - 2013/04/02
PY  - 2013
N1  - https://doi.org/10.11648/j.sjams.20130101.11
DO  - 10.11648/j.sjams.20130101.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 1
EP  - 6
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20130101.11
AB  - In classic mathematical physics course, under the local boundary conditions the Dirichlet (first kind), Neuman (second kind) and at last special case of Poincare (third kind) boundary value problems were considered for a Laplace equation being a canonic form of elliptic type of equations. Later on for a Laplace equation, under non-local boundary condition the Steklov problem was investigated in [3] and a sufficient condition for Fredholm property was found. Note that here boundary conditions contains non -local and global terms and the investigation method consist of obtaining necessary conditions, regularization of them and reducing the stated boundary problem to the system of second kind Fredholm integral equation with non-singular kernel.
VL  - 1
IS  - 1
ER  -

Copy | Download