One-Dimensional Hyperbolic Equations

2009 ◽  
pp. 113-240
Keyword(s):  
Hyperbolic Equations ◽  
One Dimensional

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.

The problem of determining the one-dimensional kernel of viscoelasticity equation with a source of explosive type

2020 ◽  
Vol 28 (1) ◽  
pp. 43-52
Author(s):  
Durdimurod Kalandarovich Durdiev ◽  
Zhanna Dmitrievna Totieva
Keyword(s):  
Inverse Problem ◽  
Hyperbolic Equations ◽  
Stability Estimate ◽  
Continuous Functions ◽  
System Of Integral Equations ◽  
One Dimensional ◽  
Weighted Norms ◽  
The Stability ◽  
The One ◽  
Global Unique Solvability

AbstractThe integro-differential system of viscoelasticity equations with a source of explosive type is considered. It is assumed that the coefficients of the equations depend only on one spatial variable. The problem of determining the kernel included in the integral terms of the equations is studied. The solution of the problem is reduced to one inverse problem for scalar hyperbolic equations. This inverse problem is replaced by an equivalent system of integral equations for unknown functions. The principle of constricted mapping in the space of continuous functions with weighted norms to the latter is applied. The theorem of global unique solvability is proved and the stability estimate of solution to the inverse problem is obtained.

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

scholarly journals Oscillation criteria for a class of partial functional-differential equations of higher order

2002 ◽  
Vol 15 (3) ◽  
pp. 255-267 ◽  
Author(s):  
Tariel Kiguradze ◽  
Takasi Kusano ◽  
Norio Yoshida
Keyword(s):  
Differential Equations ◽  
Hyperbolic Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Cylindrical Domain ◽  
One Dimensional ◽  
Beam Equations ◽  
Oscillation Problem ◽  
Functional Differential

Higher order partial differential equations with functional arguments including hyperbolic equations and beam equations are studied. Sufficient conditions are derived for every solution of certain boundary value problems to be oscillatory in a cylindrical domain. Our approach is to reduce the multi-dimensional oscillation problem to a one-dimensional problem for higher order functional differential inequalities.

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