Global nonexistence for logarithmic wave equations with nonlinear damping and distributed delay terms

Park, Sun‐Hye

doi:10.1016/j.nonrwa.2022.103691

Cited by 8 publications

(3 citation statements)

References 21 publications

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“…Here, we note that there seems to be few works that deal with viscoelastic equations with nonlinear distributed delay and damping effects. The one we find is due to Park [23], where the blow up of solution in finite time is proved.…”

Section: Introductionmentioning

confidence: 85%

A general decay criterion for a viscoelastic equation with nonlinear distributed delay and damping effects

Feng

Park

2023

Math Methods in App Sciences

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In this paper, a viscoelastic equation with nonlinear distributed delay and nonlinear damping effects is considered. Under very general conditions that do not involve differential inequalities for the kernel function, a general decay criterion is established through the perturbed energy method and properties of convex functions. We extend the stability result of wave equation with linear delay and linear damping to the nonlinear case.

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Section: Introductionmentioning

confidence: 85%

A general decay criterion for a viscoelastic equation with nonlinear distributed delay and damping effects

Feng

Park

2023

Math Methods in App Sciences

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“…Other authors, like [7], were interested in the case of such a problem in the frame of a Lamé system since it is found in quite a number of applications. In [8], the author established the global nonexistence of solutions for logarithmic wave equations with nonlinear damping and distributed delay terms. The findings contributed valuable insights into the limitations and constraints of such equations, enriching our understanding of their dynamic behavior.…”

Section: Introductionmentioning

confidence: 99%

Blow-Up of Solution of Lamé Wave Equation with Fractional Damping and Logarithmic Nonlinearity Source Terms

Benramdane,

Mezouar,

Bensaber

et al. 2023

Mathematics

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“…And also, the other way to treat this problem is to concern the decay of solutions (see,e.g. [4,19,23] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Global Attractors for a Class of Weakly Damped Wave Equations with Gradient Type Nonlinearity

Pan

Wang

Shuai

2022

J Nonlinear Math Phys

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In this paper, the main purpose is to study existence of the global attractor for the weakly damped wave equation with gradient type nonlinearity. To this end, we first verify the existence and uniqueness of global weak solution by the Galerkin method and compulsively variational method. Furthermore, we obtained the global strong solution under some mild assumptions on f. Secondly, we utilize the $$\omega$$ ω -limit compactness to show the semigroup generated by the equation has a compact, connected and invariant attractor.

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Global nonexistence for logarithmic wave equations with nonlinear damping and distributed delay terms

Cited by 8 publications

References 21 publications

A general decay criterion for a viscoelastic equation with nonlinear distributed delay and damping effects

A general decay criterion for a viscoelastic equation with nonlinear distributed delay and damping effects

Blow-Up of Solution of Lamé Wave Equation with Fractional Damping and Logarithmic Nonlinearity Source Terms

Global Attractors for a Class of Weakly Damped Wave Equations with Gradient Type Nonlinearity

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