On a class of direct and inverse problems for the Poisson equation with equality of flows on part of the boundary

Makhmud Abdysametovich Sadybekov, Aishabibi A. Dukenbayeva

2018

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DOI 10.1063/1.5082081
Data confidence 70 medium
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Abstract

We consider one class of direct and inverse stationary diffusion problems describing by the Poisson equation. The problems is considered in a model domain, chosen as a half disk. Dirichlet classical boundary conditions are set on the arc of the circle. New nonlocal boundary conditions are set on the bottom base. The first condition means an equality of flows through opposite radii, and the second condition is the proportionality of distribution densities on these radii with a variable coefficient of proportionality. An inverse problem on the solution definition to the Poisson equation and its right-hand part depending only on an angular variable are considered. The considered direct and inverse problems are well-posed.