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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 9, Pages 1583–1596 (Mi zvmmf10775)  

This article is cited in 1 scientific paper (total in 1 paper)

Mixed problem for a homogeneous wave equation with a nonzero initial velocity

A. P. Khromov

Saratov State University, Saratov, Russia

Abstract: A mixed problem for a homogeneous wave equation with fixed ends, a summable potential, and a nonzero initial velocity is studied. Using the resolvent approach and developing the Krylov method for accelerating the convergence of Fourier series, a classical solution is obtained by the Fourier method under minimal conditions on the smoothness of the initial data and a generalized solution in the case of the initial velocity represented by an arbitrary summable function is found.

Key words: Fourier method, formal solution, wave equation, resolvent.

DOI: https://doi.org/10.31857/S004446690002535-9

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English version:
Computational Mathematics and Mathematical Physics, 2018, 58:9, 1531–1543

Bibliographic databases:

UDC: 519.633
Received: 18.05.2017

Citation: A. P. Khromov, “Mixed problem for a homogeneous wave equation with a nonzero initial velocity”, Zh. Vychisl. Mat. Mat. Fiz., 58:9 (2018), 1583–1596; Comput. Math. Math. Phys., 58:9 (2018), 1531–1543

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Kurdyumov, A. P. Khromov, V. A. Khalova, “Smeshannaya zadacha dlya odnorodnogo volnovogo uravneniya s nenulevoi nachalnoi skorostyu s summiruemym potentsialom”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 20:4 (2020), 444–456  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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