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.

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 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.

Generalized solvability and optimal control for an integro-differential equation of a hyperbolic type

2021 ◽  
pp. 8-9
Author(s):  
Andrii Anikushyn ◽  
Oleksandra Zhyvolovych
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Differential Operator ◽  
Existence And Uniqueness ◽  
Generalized Solution ◽  
Hyperbolic Type ◽  
Well Posedness ◽  
Volterra Type ◽  
Integral Term ◽  
Type Integral

We consider an integro-differential operator with Volterra type integral term. We provide a priory inequalities in negative norms for certain spaces. Further, using obtained inequalities we prove well-posedness (existence and uniqueness of the (weak) generalized solution) of the corresponding boundary value problem as well as a theorem on optimal control existence.

Classical and generalized of a mixed problem– solutions for a non-homogeneous wave equation

2019 ◽  
Vol 484 (1) ◽  
pp. 18-20
Author(s):  
A. P. Khromov ◽  
V. V. Kornev
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Mixed Problem ◽  
Homogeneous Equation ◽  
Generalized Solution ◽  
Problem Solution ◽  
Homogeneous Wave ◽  
Homogeneous Wave Equation ◽  
Explicit Expressions

This study follows A.N. Krylov’s recommendations on accelerating the convergence of the Fourier series, to obtain explicit expressions of the classical mixed problem–solution for a non-homogeneous equation and explicit expressions of the generalized solution in the case of arbitrary summable functions q(x), ϕ(x), y(x), f(x, t).

scholarly journals On the solvability of parabolic and hyperbolic problems with a boundary integral condition

2002 ◽  
Vol 31 (4) ◽  
pp. 201-213 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
A Priori Estimates ◽  
Hyperbolic Equations ◽  
A Priori ◽  
Integral Condition ◽  
Generalized Solution ◽  
Boundary Integral ◽  
Analysis Method ◽  
Hyperbolic Problems ◽  
Priori Estimates ◽  
Abstract Formulation

We prove the existence, uniqueness, and the continuous dependence of a generalized solution upon the data of certain parabolic and hyperbolic equations with a boundary integral condition. The proof uses a functional analysis method based on a priori estimates established in nonclassical function spaces, and on the density of the range of the linear operator associated to the abstract formulation of the studied problem.

scholarly journals Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 94 ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Kamal Shah ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet ◽  
...  
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Condition ◽  
Hilfer Fractional Derivative ◽  
Fractional Differential ◽  
Generalized Fractional Derivative ◽  
Stability Results

This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results.

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