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On the question of the correctness of inverse problems for the inhomogeneous Helmholtz equation. (Russian. English summary) Zbl 1424.35361
Summary: In the rectangular domain, the initial-boundary value problem for the Helmholtz equation and its non-local modifications are studied and the inverse problems for finding its right-hand side are studied. The solutions of direct problems with nonlocal boundary conditions and inverse problems are constructed in explicit form as the sums of orthogonal series in the system of eigenfunctions of the one-dimensional Sturm-Liouville spectral problem. The corresponding uniqueness theorems for the solution of all set problems are proved. Sufficient conditions for boundary functions are established, which are guaranteed by the existence and stability theorems for the solution of the proposed new problem statements.
MSC:
35R30 Inverse problems for PDEs
35M13 Initial-boundary value problems for PDEs of mixed type
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