On Solutions of a Singular Viscoelastic Equation with an Integral Condition

Mecheri, Hacene; Mesloub, Saïd; Messaoudi, Salim A.

doi:10.1515/gmj.2009.761

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Cited by 7 publications

(1 citation statement)

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“…In the presence of the viscoelastic term (i.e., g = 0), Mecheri et al [15] studied the following equation…”

Section: Introductionmentioning

confidence: 99%

On decay and blow-up of solutions for a singular nonlocal viscoelastic problem with a nonlinear source term

Liu¹,

Sun²,

Li³

2016

TMNA

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In this paper we consider a singular nonlocal viscoelastic problem with a nonlinear source term and a possible damping term. We proved that if the initial data enter into the stable set, the solution exists globally and decays to zero with a more general rate, and if the initial data enter into the unstable set, the solution with non-positive initial energy as well as positive initial energy blows up in finite time. These are achieved by using the potential well theory, the modified convexity method and the perturbed energy method.

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“…In the presence of the viscoelastic term (i.e., g = 0), Mecheri et al [15] studied the following equation…”

Section: Introductionmentioning

confidence: 99%

On decay and blow-up of solutions for a singular nonlocal viscoelastic problem with a nonlinear source term

Liu¹,

Sun²,

Li³

2016

TMNA

View full text Add to dashboard Cite

show abstract

Well-posedness, asymptotic stability and blow-up results for a nonlocal singular viscoelastic problem with logarithmic nonlinearity

Di,

Qiu

2024

Z. Angew. Math. Phys.

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On the General Stability of a Viscoelastic Wave Equation with an Integral Condition

Belhannache

Messaoudi

2020

Acta Math. Appl. Sin. Engl. Ser.

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On Solutions of a Singular Viscoelastic Equation with an Integral Condition

Abstract: In this work, we use a functional analysis approach to prove the well posedness of a mixed problem with a nonclassical condition for a viscoelastic equation with dissipation. The proof is mainly based on some a priori bounds and on some density arguments.

Cited by 7 publications

References 16 publications

On decay and blow-up of solutions for a singular nonlocal viscoelastic problem with a nonlinear source term

On decay and blow-up of solutions for a singular nonlocal viscoelastic problem with a nonlinear source term

Well-posedness, asymptotic stability and blow-up results for a nonlocal singular viscoelastic problem with logarithmic nonlinearity

On the General Stability of a Viscoelastic Wave Equation with an Integral Condition

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