Vestnik SamU. Estestvenno-Nauchnaya Ser., 2016, Issue 1-2, Pages 33–45
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
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.
nonlocal problem, integral conditions, hyperbolic equation, generalized solution, dynamical conditions.
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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
\by L.~S.~Pulkina, A.~E.~Savenkova
\paper A problem with second kind integral conditions for hyperbolic equation
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
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