Well-posedness and a general decay for a nonlinear damped porous thermoelastic system with second sound

2019 ◽  
Vol 26 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Mohammad M. Al-Gharabli ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Convex Functions ◽  
Semigroup Theory ◽  
General Decay ◽  
Well Posedness ◽  
Second Sound ◽  
Nonlinear Feedback ◽  
Damping Term ◽  
General Decay Rate ◽  
One Dimensional

Abstract In this paper, we consider a one-dimensional porous thermoelastic system with second sound and nonlinear feedback. We show the well-posedness, using the semigroup theory, and establish an explicit and general decay rate result, using some properties of convex functions and the multiplier method. Our result is obtained without imposing any restrictive growth assumption on the damping term.

scholarly journals Well-posedness and energy decay of swelling porous elastic soils with a second sound and delay term

2021 ◽  
Author(s):  
Abdelli Manel ◽  
Lamine Bouzettouta ◽  
Guesmia Amar ◽  
Baibeche Sabah
Keyword(s):  
Wave Propagation ◽  
Delay Time ◽  
Elastic System ◽  
Semigroup Theory ◽  
Energy Decay ◽  
Well Posedness ◽  
Second Sound ◽  
One Dimensional ◽  
Delay Term

In this paper we consider a one-dimensional swelling porous-elastic system with second sound and delay term acting on the porous equation. Under suitable assumptions on the weight of delay, we establish the well-posedness of the system by using semigroup theory and we prove that the unique dissipation due to the delay time is strong enough to exponentially stabilize the system when the speeds of wave propagation are equal.

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 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 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 in a Timoshenko-type system with thermoelasticity with second sound

2015 ◽  
Vol 4 (4) ◽  
pp. 263-284 ◽  
Author(s):  
Mohamed Ali Ayadi ◽  
Ahmed Bchatnia ◽  
Makram Hamouda ◽  
Salim Messaoudi
Keyword(s):  
Group Theory ◽  
Type System ◽  
General Decay ◽  
Regularity Of Solutions ◽  
Well Posedness ◽  
Second Sound ◽  
Semi Group ◽  
Stability Number ◽  
Timoshenko System ◽  
Relaxation Functions

AbstractIn this article, we consider a vibrating nonlinear Timoshenko system with thermoelasticity with second sound. We discuss the well-posedness and the regularity of solutions using the semi-group theory. Moreover, we establish an explicit and general decay result for a wide class of relaxation functions, which depend on a stability number μ.

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
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