General Decay Rate for Nonlinear Thermoviscoelastic System with a Weak Damping and Nonlinear Source Term

2015 ◽  
Vol 13 (5) ◽  
pp. 3101-3120
Author(s):  
Amel Boudiaf ◽  
Salah Drabla ◽  
Fairouz Boulanouar
Keyword(s):  
Decay Rate ◽  
Source Term ◽  
General Decay ◽  
General Decay Rate ◽  
Nonlinear Source ◽  
Weak Damping

scholarly journals General Decay Rate of Solution for Love-Equation with Past History and Absorption

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1632
Author(s):  
Khaled Zennir ◽  
Mohamad Biomy
Keyword(s):  
Decay Rate ◽  
Source Term ◽  
Blow Up ◽  
Past History ◽  
Point Of View ◽  
General Decay ◽  
General Decay Rate ◽  
Infinite Memory ◽  
New Class ◽  
The Relationship

In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, a new class of nonlinear Love-equation with infinite memory in the presence of source term that takes general nonlinearity form. New minimal conditions on the relaxation function and the relationship between the weights of source term are used to show a very general decay rate for solution by certain properties of convex functions combined with some estimates. Investigations on the propagation of surface waves of Love-type have been made by many authors in different models and many attempts to solve Love’s equation have been performed, in view of its wide applicability. To our knowledge, there are no decay results for damped equations of Love waves or Love type waves. However, the existence of solution or blow up results, with different boundary conditions, have been extensively studied by many authors. Our interest in this paper arose in the first place in consequence of a query for a new decay rate, which is related to those for infinite memory ϖ in the third section. We found that the system energy decreased according to a very general rate that includes all previous results.

scholarly journals General decay rate of a weakly dissipative viscoelastic equation with a general damping

2020 ◽  
Vol 40 (6) ◽  
pp. 647-666
Author(s):  
Khaleel Anaya ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Wide Class ◽  
Nonlinear Damping ◽  
Numerical Results ◽  
General Decay ◽  
General Decay Rate ◽  
Relaxation Functions ◽  
Viscoelastic Equation

In this paper, we consider a weakly dissipative viscoelastic equation with a nonlinear damping. A general decay rate is proved for a wide class of relaxation functions. To support our theoretical findings, some numerical results are provided.

scholarly journals Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelbaki Choucha ◽  
Salah Boulaaras
Keyword(s):  
Asymptotic Behavior ◽  
Decay Rate ◽  
Energy Method ◽  
Distributed Delay ◽  
Type Equation ◽  
General Decay ◽  
Kirchhoff Equation ◽  
General Decay Rate ◽  
Kirchhoff Type ◽  
Nonlinear Viscoelastic

AbstractA nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

scholarly journals Stochastic stabilization of differential systems with general decay rate

2003 ◽  
Vol 48 (5) ◽  
pp. 397-406 ◽  
Author(s):  
Tomás Caraballo ◽  
Marı́a J. Garrido-Atienza ◽  
José Real
Keyword(s):  
Decay Rate ◽  
General Decay ◽  
Differential Systems ◽  
General Decay Rate ◽  
Stochastic Stabilization

General decay rate estimates for viscoelastic dissipative systems

2008 ◽  
Vol 68 (1) ◽  
pp. 177-193 ◽  
Author(s):  
M.M. Cavalcanti ◽  
V.N. Domingos Cavalcanti ◽  
P. Martinez
Keyword(s):  
Decay Rate ◽  
General Decay ◽  
Dissipative Systems ◽  
General Decay Rate

scholarly journals Global existence and blow-up results for a nonlinear model for a dynamic suspension bridge

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Quang-Minh Tran ◽  
Hong-Danh Pham
Keyword(s):  
Weak Solution ◽  
Global Existence ◽  
Decay Rate ◽  
Wave Equations ◽  
Source Term ◽  
Blow Up ◽  
Suspension Bridge ◽  
Nonlinear Damping ◽  
Damping Term ◽  
General Decay Rate

<p style='text-indent:20px;'>The paper deals with global existence and blow-up results for a class of fourth-order wave equations with nonlinear damping term and superlinear source term with the coefficient depends on space and time variable. In the case the weak solution is global, we give information on the decay rate of the solution. In the case the weak solution blows up in finite time, estimate the lower bound and upper bound of the lifespan of the blow-up solution, and also estimate the blow-up rate. Finally, if our problem contains an external vertical load term, a sufficient condition is also established to obtain the global existence and general decay rate of weak solutions.</p>

Stabilization in general decay rate of discrete feedback control for non-autonomous Markov jump stochastic systems

2022 ◽  
Vol 417 ◽  
pp. 126771
Author(s):  
Lichao Feng ◽  
Qiumei Liu ◽  
Jinde Cao ◽  
Chunyan Zhang ◽  
Fawaz Alsaadi
Keyword(s):  
Feedback Control ◽  
Decay Rate ◽  
Stochastic Systems ◽  
General Decay ◽  
Markov Jump ◽  
General Decay Rate
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