Classical solution of a problem with an integral condition for the one-dimensional wave equation

Moiseev, E. I.; Korzyuk, V. I.; Kozlovskaya, I. S.

doi:10.1134/s0012266114100103

“…Thus, we have a closed system of equations (4)-(6), (15), (12), (16), and (11) for determining unknown…”

Section: By Virtue Of Conditionsmentioning

confidence: 99%

An integral-boundary value problem for a partial differential equation of second order

Assanova¹

2019

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An integral-boundary value problem for a hyperbolic partial differential equation in two independent variables is considered. By introducing additional functional parameters, we investigate the solvability of the problem and develop an algorithm for finding its approximate solutions. The problem is reduced to an equivalent one, consisting of the Goursat problem for a hyperbolic equation with parameters and boundary value problems with an integral condition for ODEs with respect to the parameters entered. We propose an algorithm to find an approximate solution to the original problem, which is based on the algorithm for finding a solution to the equivalent problem. The convergence of the algorithms is proved. A coefficient criterion for the unique solvability of the integral-boundary value problem is established.

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“…Nowadays various nonlocal problems for partial differential equations are actively studied and one can find a lot of papers dealing with them; see [2,9,14,13,18] and references therein. We focus our attention on nonlocal problems with integral conditions for hyperbolic equations which have been studied in [1,3,4,6,12,9,25,17,19,23,27,28]. Systematic studies of nonlocal problems with integral conditions originated with the papers by Cannon [10] and Kamynin [16].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal problems for hyperbolic equations from the viewpoint of strongly regular boundary conditions

Pulkina

2020

ejde

3

0

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In this article, we consider a nonlocal problem for hyperbolic equation with integral conditions and show their close connection with the notion of strongly regular boundary conditions. This has an important bearing on the method of the study of solvability. We propose also a new approach which enables us to prove a unique solvability of the nonlocal problem with integral condition. For more information see https://ejde.math.txstate.edu/Volumes/2020/28/abstr.html

show abstract

“…Nowadays various nonlocal problems for partial differential equations are actively studied and one can find a lot of papers dealing with them; see [2,9,14,13,18] and references therein. We focus our attention on nonlocal problems with integral conditions for hyperbolic equations which have been studied in [1,3,4,6,12,9,25,17,19,23,27,28]. Systematic studies of nonlocal problems with integral conditions originated with the papers by Cannon [10] and Kamynin [16].…”

Section: Introductionmentioning

confidence: 99%

Stabilization of the wave equation with variable coefficients and a dynamical boundary control

Zhang

2020

ejde

0

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In this article, we consider a nonlocal problem for hyperbolic equation with integral conditions and show their close connection with the notion of strongly regular boundary conditions. This has an important bearing on the method of the study of solvability. We propose also a new approach which enables us to prove a unique solvability of the nonlocal problem with integral condition. For more information see https://ejde.math.txstate.edu/Volumes/2020/28/abstr.html

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Classical solution of a problem with an integral condition for the one-dimensional wave equation

Cited by 13 publications

References 3 publications

An integral-boundary value problem for a partial differential equation of second order

An integral-boundary value problem for a partial differential equation of second order

Nonlocal problems for hyperbolic equations from the viewpoint of strongly regular boundary conditions

Stabilization of the wave equation with variable coefficients and a dynamical boundary control

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