scholarly journals Existence and nonexistence of global solutions of the wave equation with a nonlinear boundary condition

2001 ◽  
Vol 59 (1) ◽  
pp. 153-158 ◽  
Author(s):  
Azmy S. Ackleh ◽  
Keng Deng
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Global Solutions ◽  
Existence And Nonexistence

A linear wave equation with a nonlinear boundary condition of viscoelastic type

2010 ◽  
Vol 72 (3-4) ◽  
pp. 1865-1885
Author(s):  
Le Thi Phuong Ngoc ◽  
Nguyen Anh Triet ◽  
Nguyen Thanh Long
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Linear Wave ◽  
Linear Wave Equation

RAPID FLUCTUATIONS OF SNAPSHOTS OF ONE-DIMENSIONAL LINEAR WAVE EQUATION WITH A VAN DER POL NONLINEAR BOUNDARY CONDITION

2005 ◽  
Vol 15 (02) ◽  
pp. 567-580 ◽  
Author(s):  
YU HUANG ◽  
JUN LUO ◽  
ZUOLING ZHOU
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Dynamical Behavior ◽  
Linear Wave ◽  
Van Der Pol ◽  
Linear Wave Equation ◽  
Energy Pumping ◽  
Long Run

In this paper, we consider a linear wave equation on an interval with a van der Pol nonlinear boundary condition at one end and an energy-pumping condition at the other end. We study the dynamical behavior of the Riemann invariants (u,v) of the wave equation in terms of the growth rates of the total variations of the snapshots on the spatial interval. Our main contributions here are the detection of rapid fluctuations of the snapshots of u and v in the long run. The results here sharpen those in the earlier works of [Chen et al., 2001] and [Huang, 2003].

Sign in / Sign up

Export Citation Format

Share Document