scholarly journals On the decay and blow-up of solution for a system of nonlinear viscoelastic plate equations with dissipative terms

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Jianghao Hao ◽  
Xiaoling Zhang
Keyword(s):  
Blow Up ◽  
Viscoelastic Plate ◽  
Nonlinear Viscoelastic ◽  
Plate Equations ◽  
Dissipative Terms

Blow Up of Solutions for a System of Nonlinear Viscoelastic Equations with Damping Terms in Rn

2009 ◽  
Vol 64 (3-4) ◽  
pp. 180-184
Author(s):  
Wenjun Liu ◽  
Shengqi Yub
Keyword(s):  
Initial Data ◽  
Differential Inequality ◽  
Blow Up ◽  
Coupled System ◽  
Initial Energy ◽  
Relaxation Functions ◽  
Nonlinear Viscoelastic ◽  
Linear Damping ◽  
Viscoelastic Equations ◽  
Damping And Source Terms

Abstract We consider a coupled system of nonlinear viscoelastic equations with linear damping and source terms. Under suitable conditions of the initial data and the relaxation functions, we prove a finitetime blow-up result with vanishing initial energy by using the modified energy method and a crucial lemma on differential inequality

scholarly journals On Asymptotic Behavior and Blow-Up of Solutions for a Nonlinear Viscoelastic Petrovsky Equation with Positive Initial Energy

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Gang Li ◽  
Yun Sun ◽  
Wenjun Liu
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Energy ◽  
Positive Initial Energy ◽  
Nonlinear Viscoelastic ◽  
Petrovsky Equation ◽  
Initial Boundary Value

This paper deals with the initial boundary value problem for the nonlinear viscoelastic Petrovsky equationutt+Δ2u−∫0tgt−τΔ2ux,τdτ−Δut−Δutt+utm−1ut=up−1u. Under certain conditions ongand the assumption thatm<p, we establish some asymptotic behavior and blow-up results for solutions with positive initial energy.

scholarly journals On the blow-up of the Cauchy problem of higher-order nonlinear viscoelastic wave equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mohammad Kafini
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Blow Up ◽  
Initial Energy ◽  
Higher Order ◽  
Viscoelastic Wave Equation ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Wave ◽  
The Cauchy Problem ◽  
Whole Space

<p style='text-indent:20px;'>In this paper we consider the Cauchy problem for a higher-order viscoelastic wave equation with finite memory and nonlinear logarithmic source term. Under certain conditions on the initial data with negative initial energy and with certain class of relaxation functions, we prove a finite-time blow-up result in the whole space. Moreover, the blow-up time is estimated explicitly. The upper bound and the lower bound for the blow up time are estimated.</p>

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