Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. Saratov Univ. Math. Mech. Inform.: Year: Volume: Issue: Page: Find

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

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)
References: PDF file   HTML file

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} 

• http://mi.mathnet.ru/eng/isu752
• http://mi.mathnet.ru/eng/isu/v18/i2/p157

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
•  Number of views: This page: 187 Full text: 64 References: 15