New Method of Solvability of a Three-dimensional Laplace Equation with Nonlocal Boundary Conditions
DOI:
https://doi.org/10.15407/mag12.03.185Ключові слова:
нелокальні граничні умови, тривимірне рівняння Лапласа, багатовимірний сингулярний інтеграл, необхідні умови, регуляризація, фредгольмовістьАнотація
Ввивчено розв'язки крайової задачi з нелокальними граничними умовами для тривимiрного рiвняння Лапласа. Тут граничнi умови є найбiльш поширеними i лiнiйними. Вiдзначимо, що сингулярнi iнтеграли, що входять до необхiдних умов, є багатовимiрними. Таким чином, регуляризацiя цих особливостей незрiвнянно складнiша за регуляризацiю одновимiрних сингулярних iнтегралiв. Пiсля регуляризацiї сингулярностей доведено фредгольмовiсть поставленої задачi.
Mathematical Subject Classification: 35J05, 35J40.
Посилання
N.A. Aliyev and A.A. Mehtiyev, Investigation of the Solutions of Boundary Value Problem for Cauchy–Riemann Type Equation in Confined Plane Field. — Journal Scientific News of Sumgayit State University 4 (2002), 30–34.
N.A. Aliyev and A.Kh. Abbasova, A New Approach to the Boundary Problems for Cauchy–Riemann Equation. — Journal News of Baku State University, Phys.-Math. Sci. Series 2 (2010), 49–56.
M. Jahanshahi and N.A. Aliyev, Determining of an Analytic Function on Its Analytic Domain by Cauchy–Riemann Equation with Special Kind of Boundary Conditions. — Southeast Asian Bulletin of Mathematics 1 (2004), 33–39.
N.A. Aliyev, M.H. Fatehi, and M. Jahanshahi, Analytic Solution for the Cauchy– Riemann Equation with Non-local Boundary Conditions in the First Semi-Quarter. — Quarterly Journal of Science Tarbiat Moallem University 1 (2010), 29–40.
N.A. Aliyev and M. Jahanshahi, Sufficient Conditions for Reduction of the BVP Including a Mixed PDE with Non-local Boundary Conditions to Fredholm Integral Equations. — International Journal of Mathematical Education in Science and Technology 3 (1997), 419–425.
N.A. Aliyev and M.R. Zeynalov, Steklov Problem for the First order Equation of Elliptic Type. — Journal News of Baku State University, Phys.-Math. Sci. Series 2 (2012), 12–20.
M. Sajjadmanesh, M. Jahanshahi, and N. Aliyev, Inverse Problem of the Kind of Tikhonov–Lavrentiev Including the Cauchy–Riemann Equation on a Boundary Region. Book of Abstracts, The Fourth Congress of the Turkic World Mathematical Society. Azerbaijan, Baku, 1-3 July, 2011, p. 266.
N.A. Aliyev, Y.Y. Mustafayeva, and S.M. Murtuzayeva, The Influence of the Carleman Condition on the Fredholm Property of the Boundary Value Problem for Cauchy–Riemann Equation. — Proceedings of the Institute of Applied Mathematics 2 (2012), 153–162.
N.A. Aliyev and M. Jahanshahi, Solution of Poisson’s Equation with Global, Local and Nonlocal Boundary Conditions. — International Journal of Mathematical Education in Science and Technology 2 (2002), 241–247. https://doi.org/10.1080/00207390110097551
R.V. Huseynov, N.A. Aliyev, and S.M. Murtuzayeva, Influence of Karleman Condition by Investigating Boundary Value Problems for Laplace Equation. — Trans. Natl. Acad. Sci. Azerb., Ser. Phys.-Tech. Math. Sci. 4 (2010), 73–84.
N.A. Aliev, A.Kh. Abbasova, and R.M. Zeynalov, Non-local Boundary Condition Steklov Problem for a Laplace Equation in Bounded Domain. — Science Journal of Applied Mathematics and Statistics 1 (2013), 1–6. https://doi.org/10.11648/j.sjams.20130101.11
N.A. Aliev and S.M. Hosseini, An Analysis of a Parabolic Problem with a General (Non-local and Global) Supplementary Linear Conditions. II. — Italian Journal of Pure and Applied Mathematics 13 (2003), 115–127.
N.A. Aliev and S.M. Hosseini, An Analysis of a Parabolic Problem with a General (Non-local and Global) Supplementary Linear Conditions. I. — Italian Journal of Pure and Applied Mathematics 12 (2002), 143–153.
N.A. Aliev and R.M. Aliguliyev, Boundary Value Problem for Equations of Hyperbolic Type. College of science works ”Spectral theory of differential operators” Baku, 1984, 3–9.
F.Bahrami, N.A. Aliev and S.M. Hosseini, 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 17 (2005) 91–104.
M.R. Fatemi and N.A. Aliyev, General Linear Boundary Value Problem for the Second-Order Integro-Differential Loaded Equation with Boundary Conditions Containing Both Nonlocal and Global Terms. — Journal Abstract and Applied Analysis 2010 (2010), Article ID 547526.
A.Y. Delshad Gharehgheshlaghi and N.A. Aliyev, On Fredholm Property of Boundary Value Problems for a Composite Type Model Equation with General Boundary Conditions. — Intern. J. Computer Math. (2011), 124–135.
A.Y. Delshad Gharehgheshlaghi and N.A. Aliyev, General Boundary Value Problem for the Third Order Linear Differential Equation of Composite Type. — J. Math. Phys., Anal., Geom. 2 (2012), 119–134.
M. Jahanshahi, N.A. Aliev, and S.M. Hosseini, An Analytic Method for Investigation and Solving Two-Dimensional Steady State Navier–Stokes Equations (I). — Southeast Asian Bulletin of Mathematics 33 (2009), 749–763 (1075–1089).
N.A. Aliev, Sh. Rezapour, and M.Jahanshahi, On a Mixed Problem for Navier– Stokes System in the Unit Cube. — Journal Mathematica Moravica 1 (2009), 13–24.
N.A. Aliev and A.S. Guliev, A Boundary Value Problem for the Laplace Equation in a Three-dimensional Space. — J. Proc. Azerb. Acad. Sci., Ser. Phys.-Tech. Math. Sci. 5 (1985), 53–56.
A.N. Kolmogorov and S.V. Fomin, Introductory Real Analysis. Dover Publications, New York, 1975
F.G. Trikomi, Integral Equations. Interscience Publishers, New York, 1957.
N.A. Aliyev and S.M. Hosseini, Multidimensional Singular Fredholm Integral Equations in a Finite Domain and Their Regularization. — Southeast Asian Bulletin of Mathematics 3 (2003), 395–408.
V.S. Vladimirov, Equations of Mathematical Physics. Mir, Moscow, 1981.
