The One Dimensional Wave Equation with Wentzell Boundary Conditions

2001 ◽  
Author(s):  
Angelo Favini ◽  
Gisele Ruiz Goldstein ◽  
Jerome Goldstein ◽  
Silvia Romanelli
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
One Dimensional ◽  
Wentzell Boundary Conditions ◽  
The One ◽  
Dimensional Wave

The non-autonomous wave equation with general Wentzell boundary conditions

2005 ◽  
Vol 135 (2) ◽  
pp. 317-329 ◽  
Author(s):  
Angelo Favini ◽  
Ciprian G. Gal ◽  
Gisèle Ruiz Goldstein ◽  
Jerome A. Goldstein ◽  
Silvia Romanelli
Keyword(s):  
Hilbert Space ◽  
Wave Equation ◽  
Boundary Conditions ◽  
Abstract Cauchy Problem ◽  
Regularity Conditions ◽  
Well Posedness ◽  
One Dimensional ◽  
Wentzell Boundary Conditions ◽  
Image Position ◽  
Dimensional Wave

We study the problem of the well-posedness for the abstract Cauchy problem associated to the non-autonomous one-dimensional wave equation utt = A(t)u with general Wentzell boundary conditions Here A(t)u := (a(x, t)ux)x, a(x, t) ≥ ε > 0 in [0, 1] × [0, + ∞) and βj(t) > 0, γj(t) ≥ 0, (γ0(t), γ1(t)) ≠ (0,0). Under suitable regularity conditions on a, βj, γj we prove the well-posedness in a suitable (energy) Hilbert space

Thermally corrected solutions of the one-dimensional wave equation for the laser-induced ultrasound

2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
The One ◽  
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.

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