scholarly journals STABILITY FOR A VISCOELASTIC PLATE EQUATION WITH p-LAPLACIAN

2015 ◽  
Vol 52 (3) ◽  
pp. 907-914 ◽  
Author(s):  
Sun Hye Park
Keyword(s):  
Viscoelastic Plate ◽  
Plate Equation

scholarly journals Well-posedness and asymptotic stability results for a viscoelastic plate equation with a logarithmic nonlinearity

2018 ◽  
Vol 99 (1) ◽  
pp. 50-74 ◽  
Author(s):  
Mohammad M. Al-Gharabli ◽  
Aissa Guesmia ◽  
Salim A. Messaoudi
Keyword(s):  
Asymptotic Stability ◽  
Viscoelastic Plate ◽  
Well Posedness ◽  
Plate Equation ◽  
Stability Results

Exponential stability of a mildly dissipative viscoelastic plate equation with variable density

2018 ◽  
Vol 42 (2) ◽  
pp. 733-741
Author(s):  
Xin-Guang Yang ◽  
Rawlilson de Oliveira Araujo ◽  
Ricardo de Sá Teles
Keyword(s):  
Exponential Stability ◽  
Viscoelastic Plate ◽  
Variable Density ◽  
Plate Equation

scholarly journals Global Well-Posedness and Stability for a Viscoelastic Plate Equation with a Time Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Baowei Feng
Keyword(s):  
Time Delay ◽  
Boundary Value Problem ◽  
Viscoelastic Plate ◽  
Energy Estimates ◽  
Memory Term ◽  
Well Posedness ◽  
Plate Equation ◽  
Delay Term ◽  
Galerkin Approximations ◽  
Energy Perturbation

A plate equation with a memory term and a time delay term in the internal feedback is investigated. Under suitable assumptions, we establish the global well-posedness of the initial and boundary value problem by using the Faedo-Galerkin approximations and some energy estimates. Moreover, by using energy perturbation method, we prove a general decay result of the energy provided that the weight of the delay is less than the weight of the damping.

Decay of an Extensible Viscoelastic Plate Equation with a Nonlinear Time Delay

2018 ◽  
Vol 42 (5) ◽  
pp. 2265-2285 ◽  
Author(s):  
Baowei Feng ◽  
Khaled Zennir ◽  
Lakhdar Kassah Laouar
Keyword(s):  
Time Delay ◽  
Viscoelastic Plate ◽  
Plate Equation

scholarly journals New general decay results for a viscoelastic plate equation with a logarithmic nonlinearity

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Mohammad M. Al-Gharabli
Keyword(s):  
Acta Phys ◽  
Relaxation Function ◽  
Viscoelastic Plate ◽  
General Assumption ◽  
General Decay ◽  
Minimal Condition ◽  
Plate Equation ◽  
General Energy ◽  
The Stability ◽  
Appl Math

AbstractIn this paper, we investigate the stability of the solutions of a viscoelastic plate equation with a logarithmic nonlinearity. We assume that the relaxation function g satisfies the minimal condition $$ g^{\prime }(t)\le -\xi (t) G\bigl(g(t)\bigr), $$g′(t)≤−ξ(t)G(g(t)), where ξ and G satisfy some properties. With this very general assumption on the behavior of g, we establish explicit and general energy decay results from which we can recover the exponential and polynomial rates when $G(s) = s^{p}$G(s)=sp and p covers the full admissible range $[1, 2)$[1,2). Our new results substantially improve and generalize several earlier related results in the literature such as Gorka (Acta Phys. Pol. 40:59–66, 2009), Hiramatsu et al. (J. Cosmol. Astropart. Phys. 2010(06):008, 2010), Han and Wang (Acta Appl. Math. 110(1):195–207, 2010), Messaoudi and Al-Khulaifi (Appl. Math. Lett. 66:16–22, 2017), Mustafa (Math. Methods Appl. Sci. 41(1):192–204, 2018), and Al-Gharabli et al. (Commun. Pure Appl. Anal. 18(1):159–180, 2019).

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