On the solvability of a nonlocal boundary value problem with the equality of fluxes at a part of the boundary and of the adjoint problem

Author: Moiseev E.   Ambartsumyan V.  

Publisher: MAIK Nauka/Interperiodica

ISSN: 0012-2661

Source: Differential Equations, Vol.46, Iss.5, 2010-05, pp. : 722-729

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Abstract

In the present paper, we consider a nonlocal boundary value problem for the Laplace operator in a circular sector with the equality of fluxes on the radii and with zero value of the solution on one of the radii. We also consider the adjoint problem. We prove the uniqueness of the solution of these problems and obtain an explicit form for the solution by the spectral method. When proving the solvability of the problems, we study the completeness and the basis property of systems of root functions for problems of the type of the Samarskii-Ionkin problem in L p , which can be of interest in itself.