General decay of solutions for a viscoelastic suspension bridge with nonlinear damping and a source term

2021 ◽  
Vol 72 (3) ◽  
Author(s):  
Zayd Hajjej
Keyword(s):  
Source Term ◽  
Suspension Bridge ◽  
Nonlinear Damping ◽  
General Decay ◽  
Decay Of Solutions

scholarly journals Global existence and blow-up results for a nonlinear model for a dynamic suspension bridge

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Quang-Minh Tran ◽  
Hong-Danh Pham
Keyword(s):  
Weak Solution ◽  
Global Existence ◽  
Decay Rate ◽  
Wave Equations ◽  
Source Term ◽  
Blow Up ◽  
Suspension Bridge ◽  
Nonlinear Damping ◽  
Damping Term ◽  
General Decay Rate

<p style='text-indent:20px;'>The paper deals with global existence and blow-up results for a class of fourth-order wave equations with nonlinear damping term and superlinear source term with the coefficient depends on space and time variable. In the case the weak solution is global, we give information on the decay rate of the solution. In the case the weak solution blows up in finite time, estimate the lower bound and upper bound of the lifespan of the blow-up solution, and also estimate the blow-up rate. Finally, if our problem contains an external vertical load term, a sufficient condition is also established to obtain the global existence and general decay rate of weak solutions.</p>

scholarly journals Global Existence, Asymptotic Behavior and Blow-up of Solutions for a Suspension Bridge Equation with Nonlinear Damping and Source Terms

2017 ◽  
Author(s):  
Wenjun Liu ◽  
Hefeng Zhuang
Keyword(s):  
Global Existence ◽  
Source Term ◽  
Blow Up ◽  
Suspension Bridge ◽  
Nonlinear Damping ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Damping Term ◽  
Necessary And Sufficient ◽  
Damping And Source Terms

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |ut|m-2ut and source term |u|p-2u. &nbsp;We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p&gt;m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time Tmax is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

scholarly journals Global Existence, Asymptotic Behavior and Blow-up of Solutions for a Suspension Bridge Equation with Nonlinear Damping and Source Terms

2017 ◽  
Author(s):  
Wenjun Liu ◽  
Hefeng Zhuang
Keyword(s):  
Global Existence ◽  
Source Term ◽  
Blow Up ◽  
Suspension Bridge ◽  
Nonlinear Damping ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Damping Term ◽  
Necessary And Sufficient ◽  
Damping And Source Terms

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |ut|m-2ut and source term |u|p-2u. &nbsp;We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p&gt;m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time Tmax is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

New general decay of solutions in a porous-thermoelastic system with infinite memory

2021 ◽  
Vol 500 (1) ◽  
pp. 125136
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Salim A. Messaoudi
Keyword(s):  
General Decay ◽  
Infinite Memory ◽  
Decay Of Solutions
Sign in / Sign up

Export Citation Format

Share Document