On the solvability of a nonlocal boundary value problem with opposite fluxes at a part of the boundary and of the adjoint problem |
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Authors: | E I Moiseev V E Ambartsumyan |
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Institution: | 1.Moscow State University,Moscow,Russia;2.Computer Center,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | We consider a nonlocal boundary value problem for the Laplace operator in a circular sector with opposite 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 unique solvability
of these problems and obtain the solution in an explicit form by the spectral method. As a by-product, we study the completeness
and the basis property of systems of roots functions for problems of Samarskii-Ionkin type, which may be of interest in itself. |
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