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Izv. Saratov Univ. Math. Mech. Inform., 2018, Volume 18, Issue 2, Pages 157–171 (Mi isu752)  

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

Scientific Part
Mathematics

A mixed problem for a wave equation with a nonzero initial velocity

V. P. Kurdyumov, A. P. Khromov, V. A. Khalova

Saratov State University, 83, Astrakhanskaya Str., Saratov, 410012, Russia

Abstract: We study a mixed problem for the wave equation with a continuous complex potential in the case of a nonzero initial velocity $u_t(x,0)=\psi(x)$ and two types of two-point boundary conditions: the ends are fixed and when each of the boundary boundary conditions contains a derivative with respect to $x$. A classical solution in the case $\psi(x)\in W_2^1[0,1]$ is obtained by the Fourier method with respect to the acceleration of the convergence of Fourier series by the resolvent approach with the help of A. N. Krylov's recommendations (the equation is satisfied almost everywhere). It is also shown that in the case when $\psi(x)\in L[0,1]$ the series of a formal solution for a problem with fixed ends converges uniformly in any bounded domain, and for the second problem it converges only everywhere and for both problems is a generalized solution in the uniform metric.

Key words: wave equation, formal solution, spectral problem, resolvent.

DOI: https://doi.org/10.18500/1816-9791-2018-18-2-157-171

Full text: PDF file (230 kB)
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Bibliographic databases:

UDC: 519.633

Citation: V. P. Kurdyumov, A. P. Khromov, V. A. Khalova, “A mixed problem for a wave equation with a nonzero initial velocity”, Izv. Saratov Univ. Math. Mech. Inform., 18:2 (2018), 157–171

Citation in format AMSBIB
\Bibitem{KurKhrKha18}
\by V.~P.~Kurdyumov, A.~P.~Khromov, V.~A.~Khalova
\paper A mixed problem for a wave equation with a nonzero initial velocity
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2018
\vol 18
\issue 2
\pages 157--171
\mathnet{http://mi.mathnet.ru/isu752}
\crossref{https://doi.org/10.18500/1816-9791-2018-18-2-157-171}
\elib{https://elibrary.ru/item.asp?id=35085046}


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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
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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