Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term

Al‐Gharabli, Mohammad M.; Messaoudi, Salim A.

doi:10.1007/s00028-017-0392-4

Cited by 41 publications

(37 citation statements)

References 28 publications

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“…They proved the global existence of solutions and showed that the solutions decay exponentially for a suitable initial data. Later, they extended the results to the case of nonlinear damping in the work [2]. There is not much literature for wave equations with time delay and logarithmic nonlinear source.…”

Section: Introductionmentioning

confidence: 94%

Global existence, energy decay and blow-up of solutions for wave equations with time delay and logarithmic source

Park

2020

Adv Differ Equ

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In this paper, we study the wave equation with frictional damping, time delay in the velocity, and logarithmic source of the form $$ u_{tt}(x,t) - \Delta u (x,t) + \alpha u_{t} (x,t) + \beta u_{t} (x, t- \tau ) = u(x,t) \ln \bigl\vert u(x,t) \bigr\vert ^{\gamma } . $$ u t t ( x , t ) − Δ u ( x , t ) + α u t ( x , t ) + β u t ( x , t − τ ) = u ( x , t ) ln | u ( x , t ) | γ . There is much literature on wave equations with a polynomial nonlinear source, but not much on the equations with logarithmic source. We show the local and global existence of solutions using Faedo–Galerkin’s method and the logarithmic Sobolev inequality. And then we investigate the decay rates and infinite time blow-up for the solutions through the potential well and perturbed energy methods.

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Section: Introductionmentioning

confidence: 94%

Global existence, energy decay and blow-up of solutions for wave equations with time delay and logarithmic source

Park

2020

Adv Differ Equ

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“…See, for instance, the results obtained in Komornik [2], Lagnese [3] and Lasiecka [4,5]. Al-Gharabli and Messaoudi [6] and established decay of solutions. Lu [7] investigated the nonautonomous plate-type evo- and proved that the plate is uniformly stabilizable with uniform energy decay rates with respect to the parameter γ which represents rotational force.…”

Section: Introductionmentioning

confidence: 91%

Existence and general decay estimate for a nonlinear plate problem

Mukiawa

2018

Bound Value Probl

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“…Next, we state the global existence theorem that can be established by combining arguments of [3,4,6]. Now, we introduce two functionals J (u) and I (u) ;…”

Section: Preliminariesmentioning

confidence: 99%

“…In this section, we are going to consider the decay of the solution for the problem (1) by the similar arguments as in [3,7].…”

Section: Preliminariesmentioning

confidence: 99%

Exponential Decay of Solutions for a Higher Order Wave Equation with Logarithmic Source Term

Pışkın¹,

Uysal²,

Hajrulla³

2018

Preprint

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Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term

Cited by 41 publications

References 28 publications

Global existence, energy decay and blow-up of solutions for wave equations with time delay and logarithmic source

Global existence, energy decay and blow-up of solutions for wave equations with time delay and logarithmic source

Existence and general decay estimate for a nonlinear plate problem

Exponential Decay of Solutions for a Higher Order Wave Equation with Logarithmic Source Term

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