scholarly journals Mixed problem with dynamical transmission condition for a one‐dimensional hyperbolic equation with strong dissipation

2021 ◽  
Author(s):  
Akbar B. Aliev ◽  
Gulshan Kh. Shafieva
Keyword(s):  
Hyperbolic Equation ◽  
Mixed Problem ◽  
Transmission Condition ◽  
One Dimensional

scholarly journals Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

2020 ◽  
Vol 64 (6) ◽  
pp. 657-662
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Initial Condition ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

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

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