scholarly journals Blowup for nonlinearly damped viscoelastic equations with logarithmic source and delay terms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sun-Hye Park
Keyword(s):  
Time Delay ◽  
Energy Method ◽  
Blow Up ◽  
Nonlinear Damping ◽  
Initial Energy ◽  
Damping Term ◽  
Finite Point ◽  
Source Effect ◽  
Positive Initial Energy ◽  
Viscoelastic Equations

AbstractIn this work, we investigate blowup phenomena for nonlinearly damped viscoelastic equations with logarithmic source effect and time delay in the velocity. Owing to the nonlinear damping term instead of strong or linear dissipation, we cannot apply the concavity method introduced by Levine. Thus, utilizing the energy method, we show that the solutions with not only non-positive initial energy but also some positive initial energy blow up at a finite point in time.

Blow Up of Solutions for a Viscoelastic System with Damping and Source Terms in IRn

2010 ◽  
Vol 65 (5) ◽  
pp. 392-400 ◽  
Author(s):  
Wenjun Liu
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Coupled System ◽  
Initial Energy ◽  
Source Terms ◽  
Viscoelastic System ◽  
Positive Initial Energy ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equations ◽  
Damping And Source Terms

This paper deals with a Cauchy problem for the coupled system of nonlinear viscoelastic equations with damping and source terms. We prove a new finite time blow-up result for compactly supported initial data with non-positive initial energy as well as positive initial energy by using the modified energy method and the compact support technique.

scholarly journals General Decay and Blow-Up of Solutions for a System of Viscoelastic Equations of Kirchhoff Type with Strong Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-21 ◽  
Author(s):  
Wenjun Liu ◽  
Gang Li ◽  
Linghui Hong
Keyword(s):  
Blow Up ◽  
Global Solutions ◽  
Initial Energy ◽  
General Decay ◽  
Strong Damping ◽  
Kirchhoff Type ◽  
Positive Initial Energy ◽  
Relaxation Functions ◽  
Viscoelastic Equations ◽  
Arbitrarily Positive Initial Energy

The general decay and blow-up of solutions for a system of viscoelastic equations of Kirchhoff type with strong damping is considered. We first establish two blow-up results: one is for certain solutions with nonpositive initial energy as well as positive initial energy by exploiting the convexity technique, the other is for certain solutions with arbitrarily positive initial energy based on the method of Li and Tsai. Then, we give a decay result of global solutions by the perturbed energy method under a weaker assumption on the relaxation functions.

scholarly journals Blow up of solutions for 3D quasi-linear wave equations with positive initial energy

2017 ◽  
Vol 33 (1) ◽  
pp. 97-106
Author(s):  
AMIR PEYRAVI ◽  
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Blow Up ◽  
Nonlinear Damping ◽  
Initial Energy ◽  
Nonlinear Wave Equations ◽  
Linear Wave ◽  
Positive Initial Energy ◽  
Nonlinear Anal ◽  
Klein Gordon

In this paper we investigate blow up property of solutions for a system of nonlinear wave equations with nonlinear dissipations and positive initial energy in a bounded domain in R3. Our result improves and extends earlier results in the literature such as the ones in [Zhou, J. and Mu, C., The lifespan for 3D quasilinear wave equations with nonlinear damping terms, Nonlinear Anal., 74 (2011), 5455–5466] and [Pis¸kin, E., Uniform decay and blow-up of solutions for coupled nonlinear Klein-Gordon equations with nonlinear damping terms, Math. Meth. Appl. Scie., 37 (2014), No. 18, 3036–3047] in which the nonexistence results obtained only for negative initial energy or the one in [Ye, Y., Global existence and nonexistence of solutions for coupled nonlinear wave equations with damping and source terms, Bull. Korean Math. Soc., 51 (2014), No. 6, 1697–1710] where blow up results have been not addressed. Estimate for the lower bound of the blow up time is also given.

scholarly journals A blow-up result for a system of coupled viscoelastic equations with arbitrary positive initial energy

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qian Li
Keyword(s):  
Initial Data ◽  
Finite Time ◽  
Wave Equations ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Auxiliary Function ◽  
Initial Energy ◽  
Positive Initial Energy ◽  
Viscoelastic Wave ◽  
Viscoelastic Equations

AbstractThis article is devoted to a study of the blow-up result for a system of coupled viscoelastic wave equations. By establishing a new auxiliary function and using the reduction to absurdity method, we obtain some sufficient conditions on initial data such that the solution blows up in finite time at arbitrarily high initial energy. This work generalizes and improves earlier results in the literature.

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