General decay of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping and logarithmic nonlinearity

2019 ◽  
Vol 42 (14) ◽  
pp. 4795-4814 ◽  
Author(s):  
Salah Boulaaras ◽  
Alaeddin Draifia ◽  
Khaled Zennir
Keyword(s):  
General Decay ◽  
Kirchhoff Equation ◽  
Nonlinear Viscoelastic

scholarly journals Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelbaki Choucha ◽  
Salah Boulaaras
Keyword(s):  
Asymptotic Behavior ◽  
Decay Rate ◽  
Energy Method ◽  
Distributed Delay ◽  
Type Equation ◽  
General Decay ◽  
Kirchhoff Equation ◽  
General Decay Rate ◽  
Kirchhoff Type ◽  
Nonlinear Viscoelastic

AbstractA nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

scholarly journals Exponential stability and blow up for a problem with Balakrishnan–Taylor damping

2011 ◽  
Vol 44 (1) ◽  
Author(s):  
Nasser-eddine Tatar ◽  
Abderrahmane Zaraï
Keyword(s):  
Exponential Stability ◽  
Finite Time ◽  
Blow Up ◽  
Kirchhoff Equation ◽  
Memory Term ◽  
Nonlinear Source ◽  
Polynomial Type ◽  
Nonlinear Viscoelastic ◽  
Weak Dissipation

AbstractThis work is devoted to the study of a nonlinear viscoelastic Kirchhoff equation with Balakrishnan–Taylor damping. We show that the weak dissipation produced by the memory term is strong enough to stabilize solutions exponentially. Also, we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a stronger damping.

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