scholarly journals Exact controllability of the wave equation for domains with slits and for mixed boundary conditions

1996 ◽  
Vol 2 (3) ◽  
pp. 367-386 ◽  
Author(s):  
Arnaud Heibig ◽  
◽  
Mohand Moussaoui ◽  
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Exact Controllability ◽  
Mixed Boundary Conditions

scholarly journals Classical solution of the mixed problem in the quarter of the plane for the wave equation

2019 ◽  
Vol 62 (6) ◽  
pp. 647-651
Author(s):  
V. I. Korzyuk ◽  
I. S. Kozlovskaya ◽  
V. Yu. Sokolovich
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Analytical Form ◽  
Partial Solution ◽  
Differentiable Functions ◽  
Straight Line ◽  
Straight Lines

This article presents the classical solution with mixed boundary conditions in the quarter of the plane for the wave equation in the analytical form. The boundary of the region consists of two perpendicular half-straight lines. On one of them, Cauchy’s boundary conditions are assigned. The second half-straight line is divided into two parts. Dirichlet’s condition is assigned on the straight line and Neumann’s conditions – on the half-straight line. The classical solution of the considered problem is defined in the class of double continuous differentiable functions in the quarter of the plane. To build this solution, the partial solution of the initial wave equation is written. For the assigned functions of the problem, the matching conditions are written, which are necessary and enough so that the solution of the problem would be classical and unique.

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