Computing Green's function of the initial-boundary value problem for the wave equation in a layered cylinder

2014 ◽  
Vol 91 (12) ◽  
pp. 2514-2534 ◽  
Author(s):  
V. Yakhno ◽  
D. Ozdek
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Green’S Function ◽  
Green's Function ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Layered Cylinder ◽  
Initial Boundary Value

THE GREEN'S FUNCTION FOR THE BROADWELL MODEL WITH A TRANSONIC BOUNDARY

2008 ◽  
Vol 05 (02) ◽  
pp. 279-294 ◽  
Author(s):  
CHIU-YA LAN ◽  
HUEY-ER LIN ◽  
SHIH-HSIEN YU
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Green's Function ◽  
Boundary Data ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Convergent Series ◽  
Iteration Scheme ◽  
Initial Boundary Value

We study an initial boundary value problem for the Broadwell model with a transonic physical boundary. The Green's function for the initial boundary value problem is obtained by combining the estimates of the full boundary data and the Green's function for the initial value problem. The full boundary data is constructed from the imposed boundary data through an iteration scheme. The iteration scheme is designed to separate the interaction between the boundary wave and the interior wave and leads to a convergent series in the iterative boundary estimates.

scholarly journals Application of Initial Boundary Value Problem on Logarithmic Wave Equation in Dynamics

2018 ◽  
Author(s):  
Shkelqim Hajrulla ◽  
Leonard Bezati ◽  
Fatmir Hoxha
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Boundary Value Problem ◽  
Sobolev Inequality ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Logarithmic Sobolev Inequality ◽  
Initial Boundary Value ◽  
The Galerkin Method

We introduce a class of logarithmic wave equation. We study the global existence of week solution for this class of equation. We deal with the initial boundary value problem of this class. Using the Galerkin method and the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Q-Ball Dynamic in particular.

scholarly journals Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Fosheng Wang ◽  
Chengqiang Wang
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Blow Up ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Viscoelastic Wave Equation ◽  
Frictional Damping ◽  
Viscoelastic Wave ◽  
Initial Boundary Value

We are concerned in this paper with the initial boundary value problem for a quasilinear viscoelastic wave equation which is subject to a nonlinear action, to a nonlinear frictional damping, and to a Kelvin-Voigt damping, simultaneously. By utilizing a carefully chosen Lyapunov functional, we establish first by the celebrated convexity argument a finite time blow-up criterion for the initial boundary value problem in question; we prove second by an a priori estimate argument that some solutions to the problem exists globally if the nonlinearity is “weaker,” in a certain sense, than the frictional damping, and if the viscoelastic damping is sufficiently strong.

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