Numerical solution of the mixed problem for the two dimensional wave equation

1982 ◽  
Vol 22 (2) ◽  
pp. 244-249
Author(s):  
A.A. Gladkov
Keyword(s):  
Wave Equation ◽  
Numerical Solution ◽  
Mixed Problem ◽  
Two Dimensional ◽  
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.

Boundary Feedback Stabilization of a Two-Dimensional Wave Equation

2011 ◽  
Vol 219-220 ◽  
pp. 957-960
Author(s):  
Chun Li Guo ◽  
Cheng Kang Xie ◽  
Fei Shen
Keyword(s):  
Wave Equation ◽  
Boundary Control ◽  
Closed System ◽  
Feedback Stabilization ◽  
Two Dimensional ◽  
Backstepping Method ◽  
Boundary Feedback ◽  
Dimensional Wave

Boundary control of two-dimensional wave equation on the rectangle is considered in this paper. Boundary controllers are designed through backstepping method. Stabilization of the closed system is obtained under the controllers.

scholarly journals On the Stability of Evolution Galerkin Schemes Applied to a Two‐Dimensional Wave Equation System

2006 ◽  
Vol 44 (4) ◽  
pp. 1556-1583 ◽  
Author(s):  
M. Lukáčová‐Medviďová ◽  
G. Warnecke ◽  
Y. Zahaykah
Keyword(s):  
Wave Equation ◽  
Equation System ◽  
Two Dimensional ◽  
The Stability ◽  
Dimensional Wave
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