Geodesic
Stabilization of the~solutions of the~wave equation in unbounded domains
Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 917-947

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The behaviour of the solution of the first mixed problem for the wave equation in an unbounded domain with smooth boundary is studied for large values of time. Estimates of the solution of the first boundary-value problem for the Helmholtz equation with spectral parameter in the closed upper half-plane are obtained, and uniqueness of its solution for a parameter on the real line is proved. 
@article{SM_1996_187_6_a8,
     author = {A. V. Filinovskii},
     title = {Stabilization of the~solutions of the~wave equation in unbounded domains},
     journal = {Sbornik. Mathematics},
     pages = {917--947},
     publisher = {mathdoc},
     volume = {187},
     number = {6},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_6_a8/}
}
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A. V. Filinovskii. Stabilization of the~solutions of the~wave equation in unbounded domains. Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 917-947. http://geodesic.mathdoc.fr/item/SM_1996_187_6_a8/