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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 198, Pages 50–60
DOI: https://doi.org/10.36535/0233-6723-2021-198-50-60 (Mi into873) 		 
Problem with Steklov conditions for a hyperbolic equation

A. V. Dyuzheva

Samara State Technical University
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DOI: https://doi.org/10.36535/0233-6723-2021-198-50-60
Abstract: In this paper, we consider a hyperbolic equation with one spatial variable under additional nonlocal conditions and prove the existence of a unique generalized solution. The proof is based on a priori estimates obtained, the Galerkin method, and properties of Sobolev spaces.
Keywords: hyperbolic equation, nonlocal problem, generalized solution, initial-boundary-value problem.
Document Type: Article
UDC: 517.95.6
MSC: 35L10, 35L20
Language: Russian
Citation: A. V. Dyuzheva, “Problem with Steklov conditions for a hyperbolic equation”, Differential Equations and Mathematical Physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 198, VINITI, Moscow, 2021, 50–60
Citation in format AMSBIB
\Bibitem{Dyu21}
\by A.~V.~Dyuzheva
\paper Problem with Steklov conditions for a hyperbolic equation
\inbook Differential Equations and Mathematical Physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 198
\pages 50--60
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into873}
\crossref{https://doi.org/10.36535/0233-6723-2021-198-50-60}
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