Abstract
In this paper we consider a boundary-value problem for one-dimensional hyperbolic equation with nonlocal initial data in integral form. We prove the existence and uniqueness of the generalized solution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Samarskii, A. A. “Some Problems of the Theory of Differential Equations,” Differentsial’nye Uravneniya 16, No. 11, 1925–1935 (1980).
Cannon, J. R. “The Solution of the Heat Equation Subject to the Specification of Energy,” Quart. Appl. Math., 21, No. 1, 155–160 (1963).
Gordeziani, D. G. and Avalishvili, G. A. “Solution of Nonlocal Problems for One-dimensional Oscillations of a Medium,” Mat. Model. 12, No. 1, 94–103 (2000).
Kozhanov, A. I. and Pul’kina, L. S. “On the Solvability of Boundary Value Problems with a Nonlocal Boundary Condition of Integral Form for Multidimensional Hyperbolic Equations,” Differ. Equ. 42, No. 9, 1233–1246 (2006).
Pul’kina, L. S. “Boundary-Value Problems for a Hyperbolic Equation with Nonlocal Conditions of the I and II Kind,” Russian Mathematics (Iz. VUZ) 56, No. 4, 62–69 (2012).
Pul’kina, L. S. “A Nonlocal Problemfor a Hyperbolic Equation with Integral Conditions of the First kind with Time-dependent Kernels,” Russian Mathematics (Iz. VUZ) 56, No. 10, 26–37 (2012).
Kuz’, A.M. and Ptashnik, B. I. “The Problem with Integral Conditions for the Klein-Gorgon Equation in a Class of Functions, almost Periodic with Respect to Spatial Variables,” Prikladnye Problemi Mekh. i Mat., No. 8, 41–53 (2010).
Abdrakhmanov, A. M. and Kozhanov, A. I. “A Problem with a Nonlocal Boundary Condition for a Class of Odd-order Equations,” Russian Mathematics (Iz. VUZ) 51, No. 5, 1–10 (2007).
Lukina, G. A. “Boundary-Value Problems with Integral Boundary Conditions with Respect to Time for the Third-Order Equations,” Matem. Zametki YaGU 17, No. 2, 75–97 (2010).
Prilepko, A. I. and Kostin, A. B. “Some Inverse Problems for Parabolic Equations with Final and Integral Observation,” Russian Acad. Sci. Sb. Math. 75(2), 473–490 (1992).
Cannon, J. R. and Lin, Y. P. “An Inverse Problem of Finding a Parameter in a Semi-Linear Heat Equation,” J. Math. Anal. Appl. 145(2), 470–484 (1990).
Kamynin, V. L. and Kostin, A. B. “Two Inverse Problems of the Determination of a Coefficient in a Parabolic Equation,” Differ. Equ. 46(3), 375–386 (2010).
Denisov, A.M. Introduction to the Theory of Inverse Problems (Moscow University, Moscow, 1994).
Ladyzhenskaya, O. A. Boundary-Value Problems of Mathematical Physics (Nauka, Moscow, 1973).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.V. Kirichenko, L.S. Pul’kina, 2014, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 9, pp. 17–26.
About this article
Cite this article
Kirichenko, S.V., Pul’kina, L.S. A problem with nonlocal initial data for one-dimensional hyperbolic equation. Russ Math. 58, 13–21 (2014). https://doi.org/10.3103/S1066369X14090023
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X14090023