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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 7, Pages 1156–1167
DOI: https://doi.org/10.7868/S004446691507008X (Mi zvmmf10234) 		 
This article is cited in 15 scientific papers (total in 15 papers)

A resolvent approach in the Fourier method for the wave equation: The non-selfadjoint case

V. V. Kornev, A. P. Khromov

Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russia
Full-text PDF (216 kB) Citations (15)
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DOI: https://doi.org/10.7868/S004446691507008X
Abstract: Under minimum smoothness requirements for the initial data, the Fourier method in the mixed problem for the wave equation with a complex potential is justified by using the Cauchy–Poincare technique for the contour integration of the resolvent of the eigenvalue problem. Generic boundary conditions are used; one of them contains first-order derivatives, while the other does not. In this case, even for the benchmark situation, the operator in the eigenvalue problem can have any number of generalized eigenfunctions. A substantial use is made of the technique for accelerating Fourier series due to A. N. Krylov.
Key words: mixed problem for the wave equation, Fourier method, formal solution, eigenvalue problem, resolvent approach.
Received: 18.11.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 7, Pages 1138–1149
DOI: https://doi.org/10.1134/S0965542515070088
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: V. V. Kornev, A. P. Khromov, “A resolvent approach in the Fourier method for the wave equation: The non-selfadjoint case”, Zh. Vychisl. Mat. Mat. Fiz., 55:7 (2015), 1156–1167; Comput. Math. Math. Phys., 55:7 (2015), 1138–1149
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
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