Mixed Problem with Dynamical Boundary Condition for a One-Dimensional Wave Equation with Strong Dissipation

2020 ◽  
Vol 107 (3-4) ◽  
pp. 518-521
Author(s):  
A. B. Aliev ◽  
G. Kh. Shafieva
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
One Dimensional ◽  
Dynamical Boundary Condition ◽  
Dimensional Wave

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.

scholarly journals Classical solution of the mixed problem for a one-dimensional wave equation with second-order derivatives at boundary conditions

2020 ◽  
Vol 55 (4) ◽  
pp. 406-412
Author(s):  
V. I. Korzyuk ◽  
S. N. Naumavets ◽  
V. A. Sevastyuk
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Analytical Form ◽  
Second Order ◽  
Compatibility Conditions ◽  
One Dimensional ◽  
Dimensional Wave

This paper considers the mixed problem for a one-dimensional wave equation with second-order derivatives at boundary conditions. Using the method of characteristics, a classical solution to this problem is found in analytical form. Its uniqueness is proved under the relevant compatibility conditions.

scholarly journals Mixed problem for a one-dimensional wave equation with conjugation conditions and second-order derivatives in boundary conditions

2020 ◽  
Vol 56 (3) ◽  
pp. 287-297
Author(s):  
V. I. Korzyuk ◽  
S. N. Naumavets ◽  
V. P. Serikov
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Mixed Problem ◽  
Analytical Form ◽  
Second Order ◽  
Conjugation Conditions ◽  
One Dimensional ◽  
Characteristics Method ◽  
Half Strip ◽  
Dimensional Wave

In this paper, we consider the boundary problem for the half-strip on the plane for the case of two independent variables. This mixed problem is solved for a one-dimensional wave equation with Cauchy conditions on the basis of the half-strip and boundary conditions for lateral parts of the area border containing second-order derivatives. Moreover, the conjugation conditions are specified for the required function and its derivatives for the case when the homogeneous matching conditions are not satisfied. A classical solution to this problem is found in an analytical form by the characteristics method. This solution is approved to be unique if the relevant conditions are fulfilled.

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