Abstract
To solve the Helmholtz equation interior to a bounded domain with artificial boundary, a new formulation of variational type is proposed for boundary conditions which have the property of suppressing waves reflected from the boundary. This formulation is based on the minimization of a functional constructed in a special way. Existence and uniqueness theorems are proved for a classical solution of the problem in the proposed variational formulation. It is proved that the solution of the interior problem converges uniformly to a solution of the problem posed in an unbounded domain with Sommerfeld's radiation conditions at infinity as the size of the domain increases without limit. Bibliography: 14 titles.
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