scholarly journals General decay and blow-up results of solutions for a viscoelastic wave equation with Robin-Dirichlet conditions

2020 ◽  
Vol 2020 (1) ◽  
Keyword(s):  
Wave Equation ◽  
Blow Up ◽  
General Decay ◽  
Dirichlet Conditions ◽  
Viscoelastic Wave Equation ◽  
Viscoelastic Wave

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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