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Vestnik SamGU. Estestvenno-Nauchnaya Ser., 2014, Issue 7(118), Pages 45–59 (Mi vsgu426)  
This article is cited in 3 scientific papers (total in 3 papers)

Mathematics

Necessary non-local conditions for a diffusion-wave equation

M. O. Mamchuev

Research Institute of Applied Mathematics and Automation of Kabardino-Balkar Scientific Centre of RAS, Nalchik, 360000, Russian Federation
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Abstract: In this article, diffusion-wave equation with fractional derivative in Riemann–Liouville sense is investigated. Integral operators with the Write function in the kernel associated with the investigational equation are introduced. In terms of these operators necessary non-local conditions binding traces of solution and its derivatives on the boundary of a rectangular domain are found. Necessary non-local conditions for the wave are obtained by using the limiting properties of Write function. By using the integral operator's properties the theorem of existence and uniqueness of solution of the problem with integral Samarski's condition for the diffusion-wave equation is proved. The solution is obtained in explicit form.
Keywords: diffusion-wave equation, wave equation, fractional differential equations, necessary non-local conditions, Samarski's problem, derivative of fractional order.
Received: 20.03.2014
Accepted: 20.03.2014
Document Type: Article
UDC: 517.95
Language: Russian
Citation: M. O. Mamchuev, “Necessary non-local conditions for a diffusion-wave equation”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2014, no. 7(118), 45–59
Citation in format AMSBIB
\Bibitem{Mam14}
\by M.~O.~Mamchuev
\paper Necessary non-local conditions for a diffusion-wave equation
\jour Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya
\yr 2014
\issue 7(118)
\pages 45--59
\mathnet{http://mi.mathnet.ru/vsgu426}
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    • This publication is cited in the following 3 articles:
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