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Vestnik SamU. Estestvenno-Nauchnaya Ser., 2016, Issue 1-2, Pages 33–45 (Mi vsgu499)  

Mathematics

A problem with second kind integral conditions for hyperbolic equation

L. S. Pulkinaa, A. E. Savenkovab

a Samara University, 34, Moskovskoye Shosse, Samara, 443086, Russian Federation
b Samara State Technical University, 244, Molodogvardeyskaya Street, Samara, 443100, Russian Federation

Abstract: In this paper, we consider a problem for one-dimensional hyperbolic equation with second kind integral conditions and prove unique solvability. To prove this statement we suggest a new approach. The main idea of it is that given nonlocal integral condition is equivalent with a different condition, nonlocal as well but this new condition enables us to introduce a definition of a generalized solution bazed on an integral identity and derive a priori estimates of a required solution in Sobolev space. This approach shows that integral conditions are closely connected with dynamical conditions.

Keywords: nonlocal problem, integral conditions, hyperbolic equation, generalized solution, dynamical conditions.

Full text: PDF file (333 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file
UDC: 517.956
Received: 28.03.2016

Citation: L. S. Pulkina, A. E. Savenkova, “A problem with second kind integral conditions for hyperbolic equation”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2016, no. 1-2, 33–45

Citation in format AMSBIB
\Bibitem{PulSav16}
\by L.~S.~Pulkina, A.~E.~Savenkova
\paper A problem with second kind integral conditions for hyperbolic equation
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2016
\issue 1-2
\pages 33--45
\mathnet{http://mi.mathnet.ru/vsgu499}
\elib{http://elibrary.ru/item.asp?id=29345215}


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  • Вестник Самарского государственного университета. Естественнонаучная серия
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