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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, Number 2, Pages 77–85 (Mi ivm6701)  
This article is cited in 3 scientific papers (total in 3 papers)

An over-determined boundary problem for the Helmholtz equation in a semifinite domain with a curvilinear boundary

D. N. Tumakov

Department of Applied Mathematical Physics, Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, Kazan, Russia
Full-text PDF (195 kB) Citations (3)
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Abstract: In this paper we consider an over-determined Cauchy problem for the Helmholtz equation in a semifinite domain with a piecewise smooth curvilinear boundary. Applying the Fourier transform method in the space of slow-growth distributions, we establish necessary and sufficient solvability conditions which connect the boundary functions. We construct integral representations of solutions.
Keywords: over-determined Cauchy problem, Helmholtz equation, Fourier transform, space of slow-growth distributions.
Received: 17.10.2007
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 2, Pages 66–73
DOI: https://doi.org/10.3103/S1066369X10020088
Bibliographic databases:
UDC: 517.958+537.8
Language: Russian
Citation: D. N. Tumakov, “An over-determined boundary problem for the Helmholtz equation in a semifinite domain with a curvilinear boundary”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 2, 77–85; Russian Math. (Iz. VUZ), 54:2 (2010), 66–73
Citation in format AMSBIB
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\by D.~N.~Tumakov
\paper An over-determined boundary problem for the Helmholtz equation in a~semifinite domain with a~curvilinear boundary
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 2
\pages 77--85
\mathnet{http://mi.mathnet.ru/ivm6701}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2667274}
\zmath{https://zbmath.org/?q=an:1186.35034}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 2
\pages 66--73
\crossref{https://doi.org/10.3103/S1066369X10020088}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649543396}
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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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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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