Geodesic
The resolvent approach for the wave equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 2, pp. 229-241

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Mixed problem for the wave equation (in the cases of fixed ends and periodic conditions) with minimal requirements to the initial data are studied. An approach based on the contour integration of the resolvent for the operator generated by the corresponding spectral problem is developed. This approach makes it possible to obtain a classical solution without using the asymptotics for eigenvalues or any information on eigenfunctions. 
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     author = {M. Sh. Burlutskaya and A. P. Khromov},
     title = {The resolvent approach for the wave equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {55},
     number = {2},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_2_a7/}
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M. Sh. Burlutskaya; A. P. Khromov. The resolvent approach for the wave equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 2, pp. 229-241. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_2_a7/