General decay rate for a class of weakly dissipative second‐order systems with memory

2019 ◽  
Vol 42 (8) ◽  
pp. 2842-2853 ◽  
Author(s):  
Jamilu Hashim Hassan ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Second Order ◽  
General Decay ◽  
General Decay Rate ◽  
Systems With Memory ◽  
Second Order Systems ◽  
With Memory

scholarly journals A New General Decay Rate of Wave Equation with Memory-Type Boundary Control

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Sheng Fan
Keyword(s):  
Wave Equation ◽  
Decay Rate ◽  
General Decay ◽  
Forced Oscillations ◽  
Memory Term ◽  
General Decay Rate ◽  
Damped Oscillations ◽  
Memory Type ◽  
Type Boundary ◽  
With Memory

Of interest is a wave equation with memory-type boundary oscillations, in which the forced oscillations of the rod is given by a memory term at the boundary. We establish a new general decay rate to the system. And it possesses the character of damped oscillations and tends to a finite value for a large time. By assuming the resolvent kernel that is more general than those in previous papers, we establish a more general energy decay result. Hence the result improves earlier results in the literature.

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
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