Blow-Up of Positive-Initial-Energy Solutions for an Integro-Differential Equation With Nonlinear Damping

Wu, Shun-Tang; Tsai, Long-Yi

doi:10.11650/twjm/1500406031

Cited by 26 publications

(16 citation statements)

References 17 publications

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“…This result was later improved by Messaoudi [24], to certain solutions with positive initial energy. A similar result was also obtained by Wu [25] using a different method. For the problem (1.4) in ℝ n and with m = 2, Kafini and Messaoudi [26] showed, for suitable conditions on g and initial data, that solutions with negative energy blow up in finite time.…”

Section: −ξ 1 G(t) ≤ G (T) ≤ −ξ 2 G(t) T ≥ 0supporting

confidence: 86%

Global existence and blow-up of solutions for a nonlinear wave equation with memory

Liang

Gao

2012

J Inequal Appl

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In this article, we consider the nonlinear viscoelastic equationwith initial conditions and Dirichlet boundary conditions. We first prove a local existence theorem and show, for some appropriate assumption on g and the initial data, that this solution is global with energy which decays exponentially under the potential well. Secondly, not only finite time blow-up for solutions starting in the unstable set is proved, but also under some appropriate assumptions on g and the initial data, a blow-up result with positive initial energy is established. Finally, we also prove the boundedness of global solutions for strong (ω > 0) damping case.

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Section: −ξ 1 G(t) ≤ G (T) ≤ −ξ 2 G(t) T ≥ 0supporting

confidence: 86%

Global existence and blow-up of solutions for a nonlinear wave equation with memory

Liang

Gao

2012

J Inequal Appl

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“…He showed that, under suitable conditions on g, solutions of problem (3) with initial negative energy blow up in finite time if p>m and continue to exist if m p. This result has been later pushed, by the same author [6], to certain solutions with positive initial energy. A similar result has also obtained by Wu [7] using a different method. For problem (3) in R n without the viscoelastic term (g = 0), we cite the works of Levine et al [8], Messaoudi [9], Sun and Wang [10], Yang [11] and Todorova [12,13].…”

Section: Introductionsupporting

confidence: 86%

Blow up for a Cauchy viscoelastic problem with a nonlinear dissipation of cubic convolution type

Wang

Liu

2009

Math Methods in App Sciences

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“…where F(t) = (t)G(t) + CE(t) is equivalent to E(t) because of (22), and k is a positive constant. A simple integration of (56) leads to…”

Section: General Decay Of Solutionsmentioning

confidence: 99%

General decay and blowup of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms

Pışkın

Ekinci

2019

Math Methods in App Sciences

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In this work, we consider a nonlinear system of viscoelastic equations of Kirchhoff type with degenerate damping and source terms in a bounded domain. Under suitable assumptions on the initial data, the relaxation functions gi(i = 1,2) and degenerate damping terms, we obtain global existence of solutions. Then, we prove the general decay result. Finally, we prove the finite time blow‐up result of solutions with negative initial energy. This work generalizes and improves earlier results in the literature.

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Blow-Up of Positive-Initial-Energy Solutions for an Integro-Differential Equation With Nonlinear Damping

Cited by 26 publications

References 17 publications

Global existence and blow-up of solutions for a nonlinear wave equation with memory

Global existence and blow-up of solutions for a nonlinear wave equation with memory

Blow up for a Cauchy viscoelastic problem with a nonlinear dissipation of cubic convolution type

General decay and blowup of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms

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