Email this article 
A non-local problem with integral conditions of the first kind for the string vibration equation
- Authors: Buntova Y.S.1
-
Affiliations:
- Samara National Research University
- Issue: Vol 29, No 3 (2023)
- Pages: 8-17
- Section: Mathematics
- URL: https://journals.ssau.ru/est/article/view/26968
- DOI: https://doi.org/10.18287/2541-7525-2023-29-3-8-17
- ID: 26968
Cite item
Full Text
Abstract
In this article, we consider a problem with nonlocal integral conditions of the 1st kind for the one-dimensional wave equation. The kernels of the integral conditions depend on both spatial and time variables. In order to study this problem we reduce first the integral conditions of the 1st kind to the integral conditions of the 2nd kind. Under certain additional assumptions these nonlocal conditions are equivalent. Obtained restriction on input data enable to show uniqurness of generalized solution to the problem.
About the authors
Y. S. Buntova
Samara National Research University
Author for correspondence.
Email: ynbuntova@gmail.com
ORCID iD: 0009-0003-7786-8019
postgraduate student of the Department of Differential Equations and Control Theory
Russian Federation, 34, Moskovskoye shosse, Samara, 443086, Russian FederationReferences
- Ladyzhenskaya O.A. Boundary value problems of mathematical physics. Moscow: Nauka, 1973, 407 p. Available at: https://djvu.online/file/Rh97R3cVXNcZE?ysclid=lntxmubmb390280080. (In Russ.)
- Pul’kina L.S. Boundary-value problems for a hyperbolic equation with nonlocal conditions of the I and II kind. Russian Mathematics, 2012, vol. 56, issue 4, pp. 62-–69. DOI: https://doi.org/10.3103/S1066369X12040081. (In
- English; original in Russian)
- Pul’kina L.S. Problems with non-classical conditions for hyperbolic equations: monograph. Samara: Izdatel’stvo "Samarskii universitet" , 2012, 194 p. (In Russ.)
- Dmitriev V.B. A non-local problem with integral conditions for a wave equation. Vestnik of Samara State University. Natural Science Series, 2006, no. 2 (42), pp. 15–27. Available at: http://vestniksamgu.ssau.ru/est/2006web2/math/200620002.pdf. (In Russ.)
- Cannon J.R. The solution of the heat equation subject to the specification of energy. Quarterly of Applied Mathematics, 1963, vol. 21, pp. 155–160. DOI: https://doi.org/10.1090/QAM/160437.
- Ionkin N.I. The solution of a certain boundary value problem of the theory of heat conduction with a nonclassical boundary condition. Differential Equations, 1977, vol. 13, no. 2, pp. 294–304. Available at: https://www.mathnet.ru/rus/de2993. (In Russ.)
- Kamynin L.I. A boundary value problem in the theory of heat conduction with a nonclassical boundary condition. USSR Computational Mathematics and Mathematical Physics, 1964, vol. 4, issue 6, pp. 33—59. DOI: https://doi.org/10.1016/0041-5553(64)90080-1. (In English; original in Russian)
- Pulkina L.S. The L2 solvability of a nonlocal problem with integral conditions for a hyperbolic equation. Differential Equations, 2000, vol. 36, issue 2, pp. 316-–318. DOI: https://doi.org/10.1007/BF02754219. (In English; original in Russian)
- Pulkina L.S. A non-local problem for a hyperbolic equation with integral conditions of the 1st kind with time-dependent kernels. Russian Mathematics, 2012, vol. 56, issue 10, pp. 26–37. DOI: https://doi.org/10.3103/S1066369X12100039. (in English; original in Russian)
- Pulkina L.S., Savenkova A.E. A problem with second kind integral conditions for hyperbolic equation. Vestnik of Samara University. Natural Science Series, 2016, no. 1-2, pp. 33–45. Available at: https://www.mathnet.ru/rus/vsgu499; https://www.elibrary.ru/item.asp?id=29345215. EDN: https://www.elibrary.ru/wfyota. (In Russ.)
- Pulkina L.S. A Nonlocal Problem with Integral Conditions for a Hyperbolic Equation. Differential Equations, 2004, vol. 40, no. 7, pp. 887–892. DOI: https://doi.org/10.1023/B:DIEQ.0000047025.64101.16 (In English; original in Russian)
Supplementary files
