A boundary-value problem with inclined derivatives in 3-dimensional space with the boundaries – surfaces of Liapunov type is considered in the paper. The method of investigation is based on the necessary conditions. The advantage compared to the theory of potentials is that we don‘t have limit passage, we use boundary values which are obtained from the principal relationships called necessary conditions. Remark that the directions of the derivatives given in the boundary conditions are arbitrary. Tangent directions may be some subset of the given directions.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 4) |
| DOI | 10.11648/j.sjams.20150304.14 |
| Page(s) | 188-193 |
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Inclined Derivatives, Normal Derivative, Necessary Conditions, Theory of Potentials, Fredholm Integral Equations of Second Kind
| [1] | Giraud G. Equations a integrales, Ann, Suent. Ecale narm, Super, 51, et 4, fase 3,1934, 251-372. |
| [2] | Bitsadze A.V. Boundary value problems for second elliptic equations. North-Holland, 1968. |
| [3] | Vladimirov V.S. Equations of Mathematical Physics. Mir Publisher, Moscow, 1984. |
| [4] | Bitsadze A.V. Equations of math.physics. Nauka, Moscow, 1976, 280 p. |
| [5] | Bitsadze A.V. Some classes of partial Differential Equations. Moscow, 1981,448 p. |
| [6] | Giraud G. Sur certains operations du tupe elliptigul, C.r.Acad, Sci, 200,1935, 1651-1653. |
| [7] | Mikhlin S.G. To the theory of multidimensional singular integral equations. News of Leningrad State Univ., №1, 1956, p.3-24. |
| [8] | Mikhlin S.G. Multidimensional singular integrals and integral equations. Pergamon, 1965. |
| [9] | Bitsadze A.V. Boundary value problems for systems of linear differential equations of elliptic type. News of the Academy of Sciences of Georgian SSR, 5, 8, 1944, p.761-770. |
| [10] | Verkua N.P. Systems of singular integral equations. M.-L ., Gostechizdat, 1950, p.396 . |
| [11] | Yegorov Yu.V., Kondratiev V.A. A problem with angled derivative, Math.book, 1969, vol.78, p.148- 179. |
| [12] | Bitsadze A.V. To the theory of non Fredholm elliptic boundary value problems.Dif. Eq-s with partial derivatives, Proceedings of symposium dedicated to the 60-th anniversary of acad.S.L.Sobolev, Nauka, Moscow, 1976, p.69-70. |
| [13] | Verkua I.N. New methods for solution of elliptic equations. North-Holland, Amsterdam, 1967. |
| [14] | Tovmasian N.Y. General boundary value problem for elliptic systems of second order with constant coefficients. Dif.eq., vol.2, 1966, №1, 3-23, №2, 163-171. |
| [15] | Volpert A.I. On the index of boundary value problems for systems of harmonic functions with three independent variables. DAN SSSR, 133, №1, p.13-15. |
| [16] | Paleh R. Seminar on Atie-Zinger theorem on index. Mir, Moscow, 1970, 362 p. |
| [17] | Yanushauskas A.On unconditional solvability of problems with inclined derivative. Dif. eq., vol.3, 1967, №1, p. 86-96. |
| [18] | Courant R. Rartial differential equations. New York - London, 1962. |
| [19] | Bitsadze A.V. To a problem with inclined derivative for harmonic functions in three- dimensional domains. Materials of joint Soviet-American symposium on equations in partial derivatives. Siber.depart.of SSSR Academy of Science, Novosibirsk, 1963, p.133-136. |
| [20] | Lopatinsky Ya.B. On one method of reducing boundary value problems for systems of elliptic type equations to regular integral equations. Ukr.Math.journ., 1953, vol.5,p.123-151. |
| [21] | Aliyev N., Jahanshahi M. Solution of Poisson’s equation with global, local and nonlocal boundary conditions // International Journal of Mathematical Education in Science and Technology, 33 (2002), no.2, p.241-247. |
| [22] | Jahanshahi M., Aliyev N. Determining of an analytic function on its analytic do main by Cauchy-Riemann equation with special kind of boundary conditions // Southeast Asian Bulletin Mathematics,28 (2004), no.1, p.33-39. |
| [23] | Hosseini S.M., Aliyev N. Sufficient conditions for the reduction of a BVP for PDE with non-local and global boundary conditions to Fredholm integral equations (on a rectangular domain). Applied Mathematics and Computation //147 (2004), no.3, p.669-685. |
| [24] | Magomed F. Mekhtiyev, Nihan A.Aliyev, Mehran R.Fatemi. On Fredholm property of a Boundary Value Problem for a first order equation with general boundary conditions // Transactions of National Academy of Sciences of Azerbaijan, 2009, Baku, vol.XXIX, no.4, p.221-226. |
| [25] | M.R.Fatemi and N.A.Aliyev. General Linear Boundary Value Program for the Second-Order Integro-Differential Loaded Equation with Boundary Conditions // Containing Both Nonlocal and Global Terms // Hindawi publishing Corporation. Abstract and Applied Analysis, 2010, 12 pages. |
| [26] | Aliyev N., Hosseini S.M. Cauchy problem for the Navier-Stokes equation and its reduction to a non- linear system of second kind Fredholm integral equations // International Journal of Pure and Applied Mathematics 3 (2002), no.3, p.317-324. |
| [27] | Aliev N., Rezapour Sh., Jahanshahi M. On Fefferman’s Non-existence Problems. Mathematica Moravica Journal of University of Kragujevac, Serbia, Vol. 11 (2007), p.1-7. |
| [28] | 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), p. 1-14. |
| [29] | Aliev N., Rezapour Sh., Jahanshahi M. On a mixed problem for Navier-Stokes System in the Unit Cube // Mathematica Moravica, Vol. 13-1 (2009), 13-24. |
| [30] | M. Jahanshahi, N.Aliev. An Analytic Method for Investigation and Solving Two-Dimensional Steady State Navier-Stokes Equations I // Southeast Asian Bulletin of Mathematics (2009) 33: p.749-763 (1075-1089). |
| [31] | Aliyev N., Hosseini S.M. An analysis of a parabolic problem with a general (non-local and global) supplementary linear conditions I // Italian Journal of Pure and Applied Mathematics No. 12 (2002), p.143-153 (2003) |
| [32] | Aliyev, N., Hosseini S.M. An analysis of a parabolic problem with a general (non-local and global) supplementary linear conditions II // Italian Journal of Pure and Applied Mathematics No.13 (2003), p.115-127. |
| [33] | Bahrami F., Aliyev 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 integral equations // Italian Journal of Pure and Applied Mathematics No.17 (January 2005), p. 91-104. |
| [34] | K.Ivaz, N.Aliyev. Nonlinear Two-Phase Stefan Problem // Journal of Sciences, Islamic Republic of Iran; Autumn 2007, Vol.18, No. 4, p.329-337. |
| [35] | K.Ivaz, N. Aliyev. Control of the Moving Boundary // Southeast Asian Bulletin of Mathematics (2010) 34: p. 439-450. |
APA Style
Mekhtiyev Magomed Farman, Aliyev Nihan Alipanah, Fomina Nina Ilyinichna. (2015). On One 3-Dimensional Boundary-Value Problem with Inclined Derivatives. Science Journal of Applied Mathematics and Statistics, 3(4), 188-193. https://doi.org/10.11648/j.sjams.20150304.14
ACS Style
Mekhtiyev Magomed Farman; Aliyev Nihan Alipanah; Fomina Nina Ilyinichna. On One 3-Dimensional Boundary-Value Problem with Inclined Derivatives. Sci. J. Appl. Math. Stat. 2015, 3(4), 188-193. doi: 10.11648/j.sjams.20150304.14
AMA Style
Mekhtiyev Magomed Farman, Aliyev Nihan Alipanah, Fomina Nina Ilyinichna. On One 3-Dimensional Boundary-Value Problem with Inclined Derivatives. Sci J Appl Math Stat. 2015;3(4):188-193. doi: 10.11648/j.sjams.20150304.14
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Download@article{10.11648/j.sjams.20150304.14,
author = {Mekhtiyev Magomed Farman and Aliyev Nihan Alipanah and Fomina Nina Ilyinichna},
title = {On One 3-Dimensional Boundary-Value Problem with Inclined Derivatives},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {3},
number = {4},
pages = {188-193},
doi = {10.11648/j.sjams.20150304.14},
url = {https://doi.org/10.11648/j.sjams.20150304.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150304.14},
abstract = {A boundary-value problem with inclined derivatives in 3-dimensional space with the boundaries – surfaces of Liapunov type is considered in the paper. The method of investigation is based on the necessary conditions. The advantage compared to the theory of potentials is that we don‘t have limit passage, we use boundary values which are obtained from the principal relationships called necessary conditions. Remark that the directions of the derivatives given in the boundary conditions are arbitrary. Tangent directions may be some subset of the given directions.},
year = {2015}
}
TY - JOUR T1 - On One 3-Dimensional Boundary-Value Problem with Inclined Derivatives AU - Mekhtiyev Magomed Farman AU - Aliyev Nihan Alipanah AU - Fomina Nina Ilyinichna Y1 - 2015/07/07 PY - 2015 N1 - https://doi.org/10.11648/j.sjams.20150304.14 DO - 10.11648/j.sjams.20150304.14 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 - 188 EP - 193 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20150304.14 AB - A boundary-value problem with inclined derivatives in 3-dimensional space with the boundaries – surfaces of Liapunov type is considered in the paper. The method of investigation is based on the necessary conditions. The advantage compared to the theory of potentials is that we don‘t have limit passage, we use boundary values which are obtained from the principal relationships called necessary conditions. Remark that the directions of the derivatives given in the boundary conditions are arbitrary. Tangent directions may be some subset of the given directions. VL - 3 IS - 4 ER -
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