Existence and general decay estimates for a Petrovsky-Petrovsky coupled system with nonlinear strong damping

2021 ◽  
Vol 10 (4) ◽  
pp. 645-657
Author(s):  
TAbderrahmane Beniani ◽  
Noureddine Bahri ◽  
Khaled Zennir
Keyword(s):  
Coupled System ◽  
General Decay ◽  
Decay Estimates ◽  
Strong Damping

scholarly journals Spatial Behavior of a Coupled System of Wave-Plate Type

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Gusheng Tang ◽  
Yan Liu ◽  
Wenhui Liao
Keyword(s):  
Differential Inequality ◽  
Coupled System ◽  
Second Order ◽  
Spatial Behavior ◽  
Decay Estimates ◽  
Spatial Decay ◽  
Area Measure ◽  
First Order ◽  
Wave Plate ◽  
Plate Type

The spatial behavior of a coupled system of wave-plate type is studied. We get the alternative results of Phragmén-Lindelöf type in terms of an area measure of the amplitude in question based on a first-order differential inequality. We also get the spatial decay estimates based on a second-order differential inequality.

scholarly journals A Novel Decay Rate for a Coupled System of Nonlinear Viscoelastic Wave Equations

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 203 ◽  
Author(s):  
Khaled Zennir ◽  
Sultan S. Alodhaibi
Keyword(s):  
Decay Rate ◽  
Wave Equations ◽  
Local Existence ◽  
Coupled System ◽  
Initial Energy ◽  
Energy Estimates ◽  
Contraction Mapping Theorem ◽  
Strong Damping ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Wave

The main goal of the present paper is to study the existence, uniqueness and behavior of a solution for a coupled system of nonlinear viscoelastic wave equations with the presence of weak and strong damping terms. Owing to the Faedo-Galerkin method combined with the contraction mapping theorem, we established a local existence in [ 0 , T ] . The local solution was made global in time by using appropriate a priori energy estimates. The key to obtaining a novel decay rate is the convexity of the function χ , under the special condition of the initial energy E ( 0 ) . The condition of the weights of weak and strong damping has a fundamental role in the proof. The existence of both three different damping mechanisms and strong nonlinear sources make the paper very interesting from a mathematics point of view, especially when it comes to unbounded spaces such as R n .

scholarly journals General decay estimates for a Cauchy viscoelastic wave problem

2014 ◽  
Vol 13 (4) ◽  
pp. 1541-1551 ◽  
Author(s):  
Belkacem Said-Houari ◽  
Salim A. Messaoudi
Keyword(s):  
General Decay ◽  
Decay Estimates ◽  
Wave Problem ◽  
Viscoelastic Wave

scholarly journals General Decay and Blow-Up of Solutions for a System of Viscoelastic Equations of Kirchhoff Type with Strong Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-21 ◽  
Author(s):  
Wenjun Liu ◽  
Gang Li ◽  
Linghui Hong
Keyword(s):  
Blow Up ◽  
Global Solutions ◽  
Initial Energy ◽  
General Decay ◽  
Strong Damping ◽  
Kirchhoff Type ◽  
Positive Initial Energy ◽  
Relaxation Functions ◽  
Viscoelastic Equations ◽  
Arbitrarily Positive Initial Energy

The general decay and blow-up of solutions for a system of viscoelastic equations of Kirchhoff type with strong damping is considered. We first establish two blow-up results: one is for certain solutions with nonpositive initial energy as well as positive initial energy by exploiting the convexity technique, the other is for certain solutions with arbitrarily positive initial energy based on the method of Li and Tsai. Then, we give a decay result of global solutions by the perturbed energy method under a weaker assumption on the relaxation functions.

scholarly journals General decay for weak viscoelastic equation of Kirchhoff type containing Balakrishnan-Taylor damping with nonlinear delay and acoustic boundary conditions

2021 ◽  
Author(s):  
Mi Jin Lee ◽  
Jong-Yeoul Park ◽  
Jum-Ran Kang
Keyword(s):  
Boundary Conditions ◽  
Energy Decay ◽  
General Decay ◽  
Lyapunov Functionals ◽  
Decay Estimates ◽  
Acoustic Boundary Conditions ◽  
Kirchhoff Type ◽  
General Energy ◽  
Viscoelastic Equation ◽  
Nonlinear Delay

In this paper, we consider the general energy decay for weak viscoelastic equation of Kirchhoff type containing Balakrishnan-Taylor damping with nonlinear delay and acoustic boundary conditions. By introducing suitable energy and Lyapunov functionals, we establish the general decay estimates for the energy, which depends on the behavior of both sigma and g.

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