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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 471, Pages 76–85 (Mi znsl6625)  
This article is cited in 3 scientific papers (total in 3 papers)

On the Bateman–Hörmander solution of the wave equation, having a singularity at a running point

A. S. Blagoveshchenskya, A. M. Tagirdzhanovab, A. P. Kiselevcd

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Electrotechnical University, St. Petersburg, Russia
c Steklov Mathematical Institute, St. Petersburg Branch, St. Petersburg, Russia
d Institute of Mechanical Engineering RAS, St. Petersburg, Russia
Full-text PDF (299 kB) Citations (3)
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Abstract: Hörmander have presented a remarkable example of a solution of the homogeneous wave equation, which has a singularity at a running point. We are concerned with analytic investigation of this solution for the case of three spatial variables. We describe its support, study its behavior near the singular point and establish its local integrability. We observe that the Hörmander solution is a specialization of a solution found by Bateman five decades in advance.
Key words and phrases: wave equation, explicit solutions, solutions with a singularity at a running point, Bateman solution, Hörmander solution.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00529
This work was supported in part by Russian Foundation for Basic Research grant No. 17-01-00529.
Received: 01.11.2018
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 243, Issue 5, Pages 682–688
DOI: https://doi.org/10.1007/s10958-019-04569-3
Bibliographic databases:
Document Type: Article
UDC: 517
Language: English
Citation: A. S. Blagoveshchensky, A. M. Tagirdzhanov, A. P. Kiselev, “On the Bateman–Hörmander solution of the wave equation, having a singularity at a running point”, Mathematical problems in the theory of wave propagation. Part 48, Zap. Nauchn. Sem. POMI, 471, POMI, St. Petersburg, 2018, 76–85; J. Math. Sci. (N. Y.), 243:5 (2019), 682–688
Citation in format AMSBIB
\Bibitem{BlaTagKis18}
\by A.~S.~Blagoveshchensky, A.~M.~Tagirdzhanov, A.~P.~Kiselev
\paper On the Bateman--H\"ormander solution of the wave equation, having a~singularity at a~running point
\inbook Mathematical problems in the theory of wave propagation. Part~48
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 471
\pages 76--85
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6625}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 243
\issue 5
\pages 682--688
\crossref{https://doi.org/10.1007/s10958-019-04569-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074979042}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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