Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain
Science Journal of Applied Mathematics and Statistics
Volume 1, Issue 1, April 2013, Pages: 1-6
Received: Mar. 9, 2013;
Published: Apr. 2, 2013
Views 4391 Downloads 233
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
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  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.
Aliev Nehan Ali,
Abbasova Aygun Khanlar,
Zeynalov Ramin M.,
Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain, Science Journal of Applied Mathematics and Statistics.
Vol. 1, No. 1,
2013, pp. 1-6.
Courant R., Partial Equations.,М., "Мir" publishing house, 1964, 830 рp.
Vladimirov V.S., Equations of mathematical physics. M., "Nauka" publishing house, 1981, 512 pр.
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.
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.
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.
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.
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.
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.
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.
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..
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.