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The resolvent approach for the wave equation

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Abstract

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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Authors and Affiliations

  1. Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006, Russia

    M. Sh. Burlutskaya

  2. Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russia

    A. P. Khromov

Authors
  1. M. Sh. Burlutskaya
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  2. A. P. Khromov
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Corresponding author

Correspondence to M. Sh. Burlutskaya.

Additional information

Original Russian Text © M.Sh. Burlutskaya, A.P. Khromov, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 2, pp. 229–241.

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Burlutskaya, M.S., Khromov, A.P. The resolvent approach for the wave equation. Comput. Math. and Math. Phys. 55, 227–239 (2015). https://doi.org/10.1134/S0965542515020050

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  • DOI: https://doi.org/10.1134/S0965542515020050

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