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 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.

An alternating motion with stops and the related planar, cyclic motion with four directions

2003 ◽  
Vol 35 (4) ◽  
pp. 1153-1168 ◽  
Author(s):  
S. Leorato ◽  
E. Orsingher ◽  
M. Scavino
Keyword(s):  
Hyperbolic Equation ◽  
Order Statistics ◽  
Differential System ◽  
Fourth Order ◽  
Random Motion ◽  
One Dimensional ◽  
Cyclic Motion ◽  
Order Hyperbolic Equation

In this paper we study a planar random motion (X(t), Y(t)), t>0, with orthogonal directions taken cyclically at Poisson paced times. The process is split into one-dimensional motions with alternating displacements interrupted by exponentially distributed stops. The distributions of X = X(t) (conditional and nonconditional) are obtained by means of order statistics and the connection with the telegrapher's process is derived and discussed. We are able to prove that the distributions involved in our analysis are solutions of a certain differential system and of the related fourth-order hyperbolic equation.

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).

An alternating motion with stops and the related planar, cyclic motion with four directions

2003 ◽  
Vol 35 (04) ◽  
pp. 1153-1168 ◽  
Author(s):  
S. Leorato ◽  
E. Orsingher ◽  
M. Scavino
Keyword(s):  
Hyperbolic Equation ◽  
Order Statistics ◽  
Differential System ◽  
Fourth Order ◽  
Random Motion ◽  
One Dimensional ◽  
Cyclic Motion ◽  
Order Hyperbolic Equation

In this paper we study a planar random motion (X(t),Y(t)),t>0, with orthogonal directions taken cyclically at Poisson paced times. The process is split into one-dimensional motions with alternating displacements interrupted by exponentially distributed stops. The distributions ofX=X(t) (conditional and nonconditional) are obtained by means of order statistics and the connection with the telegrapher's process is derived and discussed. We are able to prove that the distributions involved in our analysis are solutions of a certain differential system and of the related fourth-order hyperbolic equation.

scholarly journals A MIXED PROBLEM FOR THE FOUR-ORDER ONE-DIMENSIONAL HYPERBOLIC EQUATION WITH PERIODIC CONDITIONS

2018 ◽  
Vol 54 (2) ◽  
pp. 135-148
Author(s):  
V. I. Korzyuk ◽  
Nguyen Van Vinh
Keyword(s):  
Hyperbolic Equation ◽  
Classical Solution ◽  
Differential Operators ◽  
Hyperbolic Equations ◽  
One Dimensional ◽  
First Order ◽  
Mixed Problems ◽  
Uniqueness Of The Solution ◽  
Different Characteristics ◽  
Well Posed

This article considers a classical solution of the boundary problem for the four-order strictly hyperbolic equation with four different characteristics. Note that the well-posed statement of mixed problems for hyperbolic equations not only depends on the number of characteristics, but also on their location. The operator appearing in the equation involves a composition of first-order differential operators. The equation is defined in the half-strip of two independent variables. There are Cauchy’s conditions at the domain bottom and periodic conditions at other boundaries. Using the method of characteristics, the analytic solution of the considered problem is obtained. The uniqueness of the solution is proved. We have also noted that the solution in the whole given domain is a composition of the solutions obtained in some subdomains. Thus, for the obtained classical solution to possess required smoothness, the values of these piecewise solutions, as well as their derivatives up to the fourth order must coincide at the boundary of these subdomains. A classical solution is understood as a function that is defined everywhere at all closure points of a given domain and has all classical derivatives entering the equation and the conditions of the problem.

On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order

2008 ◽  
Vol 15 (3) ◽  
pp. 555-569
Author(s):  
Tariel Kiguradze
Keyword(s):  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Hyperbolic Equation ◽  
Well Posedness ◽  
Nonlinear Hyperbolic Equations ◽  
Right Hand

Abstract In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation 𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢) with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered. Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.

On inference in a one-dimensional mosaic and an M/G/∞ queue

1985 ◽  
Vol 17 (01) ◽  
pp. 210-229
Author(s):  
Peter Hall
Keyword(s):  
Poisson Process ◽  
Segment Length ◽  
One Dimensional ◽  
Estimation Procedures ◽  
The One

Suppose segments are distributed at random along a line, their locations being determined by a Poisson process. In the case where segment length is fixed, we compare efficiencies of several different estimates of Poisson intensity. The case of random segment length is also considered, and there we study estimation procedures based on empiric properties. The one-dimensional mosaic may be viewed as an M/G/∞ queue.

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