scholarly journals ON A BOUNDARY VALUE PROBLEM WITH NONLOCAL IN TIME CONDITIONS FOR A ONE-DIMENSIONAL HYPERBOLIC EQUATION

2017 ◽  
Vol 19 (6) ◽  
pp. 31-39
Author(s):  
S.V. Kirichenko
Keyword(s):  
Initial Data ◽  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Form ◽  
Generalized Solution ◽  
One Dimensional

In this article, the boundary value problem for hyperbolic equation with nonlocal initial data in integral form is considered. Existence and uniqueness of generalized solution are proved.

scholarly journals On the Existence of Eigenvalues of a Boundary Value Problem with Transmitting Condition of the Integral Form for a Parabolic-Hyperbolic Equation

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1030
Author(s):  
Abdumauvlen Berdyshev ◽  
Alberto Cabada ◽  
Erkinjon Karimov
Keyword(s):  
Boundary Value Problem ◽  
Integral Representation ◽  
Hyperbolic Equation ◽  
Boundary Value ◽  
Functional Space ◽  
Integral Form ◽  
Characteristic Line ◽  
Nuclear Operator ◽  
Local Boundary ◽  
Strong Solvability

In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Theorem on strong solvability of the considered problem has been proved and integral representation of the solution is obtained in a functional space. Using Lidskii Theorem on coincidences of matrix and spectral traces of nuclear operator and Gaal’s formula for evaluating traces of nuclear operator, which is represented as a product of two Hilbert-Schmidt operators, we prove the existence of eigenvalues of the considered problem.

On One Boundary Value Problem for a Nonlinear Equation with the Iterated Wave Operator in the Principal Part

2008 ◽  
Vol 15 (3) ◽  
pp. 541-554
Author(s):  
Sergo Kharibegashvili ◽  
Bidzina Midodashvili
Keyword(s):  
Nonlinear Equation ◽  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Wave Operator ◽  
Principal Part ◽  
Boundary Value ◽  
Power Nonlinearity ◽  
Spatial Dimensionality ◽  
Uniqueness Of A Solution

Abstract One boundary value problem for a hyperbolic equation with power nonlinearity and the iterated wave operator in the principal part is considered in a conical domain. Depending on the index of nonlinearity and spatial dimensionality of the equation the question on the existence and uniqueness of a solution of a boundary value problem is investigated. The question as to the absence of a solution of this problem is also considered.

scholarly journals INITIAL-BOUNDARY VALUE PROBLEM FOR ONE-DIMENSION HYPERBOLIC EQUATION WITH INTEGRAL BOUNDARY CONDITION

2017 ◽  
Vol 17 (8) ◽  
pp. 95-101
Author(s):  
M.V. Strigun
Keyword(s):  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Boundary Value ◽  
Integral Condition ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Generalized Solution ◽  
Integral Boundary ◽  
Nonlocal Integral Condition ◽  
Initial Boundary Value

In this paper, we study an initial-boundary value problem with nonlocal integral condition for a hyperbolic equation. The existence and uniqueness of a generalized solution of the problem is proved.

scholarly journals On One Damping Problem for a Nonstationary Control System with Aftereffect

2019 ◽  
Vol 65 (4) ◽  
pp. 547-556
Author(s):  
A. S. Adkhamova ◽  
A. L. Skubachevskii
Keyword(s):  
Control System ◽  
Boundary Value Problem ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Neutral Type ◽  
Generalized Solution ◽  
Matrix Coefficients ◽  
Nonlocal Functional ◽  
Several Delays

We consider a control system described by the system of differential-difference equations of neutral type with variable matrix coefficients and several delays. We establish the relation between the variational problem for the nonlocal functional describing the multidimensional control system with delays and the corresponding boundary-value problem for the system of differential-difference equations. We prove the existence and uniqueness of the generalized solution of this boundary-value problem.

scholarly journals An Initial Boundary Value Problem for the Zakharov Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Quankang Yang ◽  
Charles Bu
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Zakharov Equation ◽  
One Dimensional ◽  
Global Strong Solution ◽  
The One ◽  
Initial Boundary Value

This paper studies an inhomogeneous initial boundary value problem for the one-dimensional Zakharov equation. Existence and uniqueness of the global strong solution are proved by Galerkin’s method and integral estimates.

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