Geodesic
On the uniqueness and non-uniqueness of solutions of boundary-contact acoustic problems
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 21-32

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The infinite acoustic waveguide with an elastic partition and rigid sides and the waveguide with elastic sides and rigid partition are considered. The existence of the eigenfunction of the boundary problem in the first case and uniqueness of the solution of the boundary problem in the second case are determined. The plate being in a medium and supported by a rib of rigidity is considered. The case of a periodical set of ribs is also discussed. The uniqueness of the solution is tdetermined in the both cases. 
@article{ZNSL_1983_128_a2,
     author = {B. P. Belinskii},
     title = {On the uniqueness and non-uniqueness of solutions of boundary-contact acoustic problems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {21--32},
     publisher = {mathdoc},
     volume = {128},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a2/}
}
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B. P. Belinskii. On the uniqueness and non-uniqueness of solutions of boundary-contact acoustic problems. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 21-32. http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a2/