scholarly journals Hyperbolic Equations with Unknown Coefficients

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1539
Author(s):  
Aleksandr I. Kozhanov
Keyword(s):  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Integral Condition ◽  
Uniqueness Theorems ◽  
Regular Solutions ◽  
Final Data ◽  
Order Hyperbolic Equation ◽  
Weak Derivatives ◽  
Second Order Hyperbolic Equation

We study the solvability of nonlinear inverse problems of determining the low order coefficients in the second order hyperbolic equation. The overdetermination condition is specified as an integral condition with final data. Existence and uniqueness theorems for regular solutions are proved (i.e., for solutions having all weak derivatives in the sense of Sobolev, occuring in the equation).

scholarly journals On a class of singular hyperbolic equation with a weighted integral condition

1999 ◽  
Vol 22 (3) ◽  
pp. 511-519 ◽  
Author(s):  
Said Mesloub ◽  
Abdelfatah Bouziani
Keyword(s):  
Hyperbolic Equation ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Nonlocal Condition ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Priori Estimate ◽  
Weighted Integral

In this paper, we study a mixed problem with a nonlocal condition for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.

scholarly journals Non-local problem with integral conditions for the three-dimensional high order hyperbolic equations

2020 ◽  
pp. 51-62
Author(s):  
Ш.Ш. Юсубов
Keyword(s):  
Integral Equation ◽  
Hyperbolic Equation ◽  
Hyperbolic Equations ◽  
Three Dimensional ◽  
High Order ◽  
Mixed Derivative ◽  
Local Problem ◽  
Integral Conditions ◽  
Order Hyperbolic Equation ◽  
Non Local

В работе для трехмерного гиперболического уравнения высокого порядка с доминирующей смешанной производной исследуется разрешимость нелокальной задачи с интегральными условиями. Поставленная задача сводится к интегральному уравнению и с помощью априорных оценок доказывается существование единственного решения. In the work the solvability of the non-local problem with integral conditions is investigated for the three-dimensional high order hyperbolic equation with dominated mixed derivative. The problem is reduced to the integral equation and existence of the solution is proved by the help of aprior estimations.

On a Spatial Problem of Darboux Type for a Second-Order Hyperbolic Equation

1995 ◽  
Vol 2 (3) ◽  
pp. 299-311
Author(s):  
S. Kharibegashvili
Keyword(s):  
Sobolev Space ◽  
Hyperbolic Equation ◽  
Unique Solvability ◽  
Second Order ◽  
Spatial Problem ◽  
Order Hyperbolic Equation ◽  
Second Order Hyperbolic Equation

Abstract The theorem of unique solvability of a spatial problem of Darboux type in Sobolev space is proved for a second-order hyperbolic equation.

The Equations of Markovian Random Evolution on the Line

1998 ◽  
Vol 35 (1) ◽  
pp. 27-35 ◽  
Author(s):  
Alexander Kolesnik
Keyword(s):  
Poisson Process ◽  
Hyperbolic Equation ◽  
Explicit Form ◽  
General Model ◽  
Hyperbolic Equations ◽  
Random Evolution ◽  
One Dimensional ◽  
Order Hyperbolic Equation

We consider a general model of one-dimensional random evolution with n velocities and rates of a switching Poisson process (n ≥ 2). A governing nth-order hyperbolic equation in a determinant form is given. For two important particular cases it is written in an explicit form. Some known hyperbolic equations are obtained as particular cases of the general model

The Equations of Markovian Random Evolution on the Line

1998 ◽  
Vol 35 (01) ◽  
pp. 27-35 ◽  
Author(s):  
Alexander Kolesnik
Keyword(s):  
Poisson Process ◽  
Hyperbolic Equation ◽  
Explicit Form ◽  
General Model ◽  
Hyperbolic Equations ◽  
Random Evolution ◽  
One Dimensional ◽  
Order Hyperbolic Equation

We consider a general model of one-dimensional random evolution with n velocities and rates of a switching Poisson process (n ≥ 2). A governing nth-order hyperbolic equation in a determinant form is given. For two important particular cases it is written in an explicit form. Some known hyperbolic equations are obtained as particular cases of the general model

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