scholarly journals Finite time blow-up for a wave equation with dynamic boundary condition at critical and high energy levels in control systems

2020 ◽  
Vol 28 (1) ◽  
pp. 91-102 ◽  
Author(s):  
Xiaoqiang Dai ◽  
◽  
Chao Yang ◽  
Shaobin Huang ◽  
Tao Yu ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Control Systems ◽  
Finite Time ◽  
Blow Up ◽  
Energy Levels ◽  
High Energy ◽  
Dynamic Boundary Condition ◽  
Dynamic Boundary

scholarly journals Global existence and blow up of solution for semi-linear hyperbolic equation with the product of logarithmic and power-type nonlinearity

2020 ◽  
Vol 40 (1) ◽  
pp. 111-130
Author(s):  
Wei Lian ◽  
Md Salik Ahmed ◽  
Runzhang Xu
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Finite Time ◽  
Blow Up ◽  
Energy Levels ◽  
Potential Well ◽  
Power Type ◽  
Potential Wells ◽  
Linear Hyperbolic Equation ◽  
Semilinear Wave Equation

In this paper we consider the semilinear wave equation with the multiplication of logarithmic and polynomial nonlinearities. We establish the global existence and finite time blow up of solutions at three different energy levels (\(E(0)\lt d\), \(E(0)=d\) and \(E(0)\gt 0\)) using potential well method. The results in this article shed some light on using potential wells to classify the solutions of the semilinear wave equation with the product of polynomial and logarithmic nonlinearity.

Global solutions and finite time blow-up for fourth order nonlinear damped wave equation

2018 ◽  
Vol 59 (6) ◽  
pp. 061503 ◽  
Author(s):  
Runzhang Xu ◽  
Xingchang Wang ◽  
Yanbing Yang ◽  
Shaohua Chen
Keyword(s):  
Wave Equation ◽  
Fourth Order ◽  
Finite Time ◽  
Blow Up ◽  
Global Solutions ◽  
Damped Wave Equation ◽  
Nonlinear Damped Wave Equation
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