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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.

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UDC: 517.956

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}