scholarly journals PROBLEM WITH NONLOCAL INTEGRAL CONDITION FOR PSEUDOHYPERBOLIC EQUATION OF THE FOURTH-ORDER

2017 ◽  
Vol 20 (3) ◽  
pp. 46-55
Author(s):  
S.V. Kirichenko
Keyword(s):  
Fourth Order ◽  
Existence And Uniqueness ◽  
Integral Condition ◽  
Generalized Solution ◽  
Pseudohyperbolic Equation ◽  
Nonlocal Integral Condition

In this article, we study a problem for a multimensional pseudohyperbolic equation of the fourth-order with an integral condition. Existence and uniqueness of a generalized solution is proved.

scholarly journals ON CERTAIN NONLOCAL PROBLEM FOR HYPERBOLIC EQUATION WITH INTEGRAL CONDITIONS OF THE FIRST KIND

2017 ◽  
Vol 17 (5) ◽  
pp. 29-36
Author(s):  
A.V. Duzheva
Keyword(s):  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Nonlocal Problem ◽  
Integral Condition ◽  
Generalized Solution ◽  
Integral Conditions

In this article, we consider a nonlocal problem for hyperbolic equation with integral conditions of the first kind. The main goal of this article is to show the method which allows to reduce posed problem to the problem with integral condition of the second kind. Existence and uniqueness of generalized solution is proved.

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 A PROBLEM WITH SECOND KIND INTEGRAL CONDITIONS FOR HYPERBOLIC EQUATION

2017 ◽  
Vol 22 (1-2) ◽  
pp. 33-45
Author(s):  
L. S. Pulkina ◽  
A. E. Savenkova
Keyword(s):  
Hyperbolic Equation ◽  
A Priori Estimates ◽  
A Priori ◽  
Main Idea ◽  
Integral Condition ◽  
Generalized Solution ◽  
Integral Conditions ◽  
Priori Estimates ◽  
Nonlocal Integral Condition ◽  
Definition Of

In this paper, we consider a problem for one-dimensional hyperbolic equation with second kind integral conditions and prove unique solvability. To prove this statement we suggest a new approach. The main idea of it is that given nonlocal integral condition is equivalent with a different condition, nonlocal as well but this new condition enables us to introduce a definition of a generalized solution bazed on an integral identity and derive a priori estimates of a required solution in Sobolev space. This approach shows that integral conditions are closely connected with dynamical conditions.

scholarly journals A MIXED PROBLEM WITH INTEGRAL CONDITION FOR A DEGENERATIVE EQUATION OF THE HYPERBOLIC TYPE

2017 ◽  
Vol 17 (8) ◽  
pp. 29-36
Author(s):  
S.V. Kirichenko
Keyword(s):  
Mixed Problem ◽  
Existence And Uniqueness ◽  
Integral Condition ◽  
Generalized Solution ◽  
Hyperbolic Type ◽  
Degenerate Equation

In this article, the mixed problem for the hyperbolic degenerate equation with an integral condition is considered. The existence and uniqueness of a generalized solution are proved.

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
Author(s):  
B. Bandyrskii ◽  
I. Lazurchak ◽  
V. Makarov ◽  
M. Sapagovas
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Integral Condition ◽  
Second Order ◽  
Computational Results ◽  
Discrete Method ◽  
Complex Eigenvalues ◽  
Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

scholarly journals On a time fractional diffusion with nonlocal in time conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nguyen Hoang Tuan ◽  
Nguyen Anh Triet ◽  
Nguyen Hoang Luc ◽  
Nguyen Duc Phuong
Keyword(s):  
Fourier Series ◽  
Diffusion Equation ◽  
Convergence Rate ◽  
Exact Solutions ◽  
Mild Solution ◽  
Integral Condition ◽  
Fractional Diffusion ◽  
Well Posedness ◽  
Nonlocal Integral Condition ◽  
Regularized Solution

AbstractIn this work, we consider a fractional diffusion equation with nonlocal integral condition. We give a form of the mild solution under the expression of Fourier series which contains some Mittag-Leffler functions. We present two new results. Firstly, we show the well-posedness and regularity for our problem. Secondly, we show the ill-posedness of our problem in the sense of Hadamard. Using the Fourier truncation method, we construct a regularized solution and present the convergence rate between the regularized and exact solutions.

scholarly journals Finite Difference Method for Hyperbolic Equations with the Nonlocal Integral Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Necmettin Aggez
Keyword(s):  
Space Variable ◽  
Hyperbolic Equations ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Variable Coefficients ◽  
Difference Schemes ◽  
Order Difference ◽  
One Dimensional ◽  
Nonlocal Integral Condition ◽  
Multidimensional Hyperbolic Equations

The stable difference schemes for the approximate solution of the nonlocal boundary value problem for multidimensional hyperbolic equations with dependent in space variable coefficients are presented. Stability of these difference schemes and of the first- and second-order difference derivatives is obtained. The theoretical statements for the solution of these difference schemes for one-dimensional hyperbolic equations are supported by numerical examples.

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