Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 229, Pages 83–89
DOI: https://doi.org/10.36535/0233-6723-2023-229-83-89 (Mi into1237) 		 
Generalized mixed problem for the simplest wave equation and its applications

A. P. Khromov

N. G. Chernyshevsky Saratov State University, Faculty of Mathematics and Mechanics
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DOI: https://doi.org/10.36535/0233-6723-2023-229-83-89
Abstract: In this paper, we present results for generalized homogeneous and inhomogeneous mixed problems for the wave equation based on the operation of integrating a divergent series of a formal solution using the method of separation of variables. A solution to the generalized mixed problem for an inhomogeneous equation is found under the assumption that the function characterizing the inhomogeneity is locally summable. As an application, a mixed problem with nonzero potential is considered.
Keywords: divergent series, wave equation, mixed problem
Document Type: Article
UDC: 517.96; 517.984
MSC: 35Mxx
Language: Russian
Citation: A. P. Khromov, “Generalized mixed problem for the simplest wave equation and its applications”, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 229, VINITI, Moscow, 2023, 83–89
Citation in format AMSBIB
\Bibitem{Khr23}
\by A.~P.~Khromov
\paper Generalized mixed problem for the simplest wave equation and its applications
\inbook Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 229
\pages 83--89
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1237}
\crossref{https://doi.org/10.36535/0233-6723-2023-229-83-89}
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