Well-posedness and general decay of a nonlinear damping porous-elastic system with infinite memory

2020 ◽  
Vol 61 (2) ◽  
pp. 021505 ◽  
Author(s):  
Houssem Eddine Khochemane ◽  
Abdelhak Djebabla ◽  
Salah Zitouni ◽  
Lamine Bouzettouta
Keyword(s):  
Elastic System ◽  
Nonlinear Damping ◽  
General Decay ◽  
Well Posedness ◽  
Infinite Memory

General decay of a nonlinear damping porous-elastic system with past history

2019 ◽  
Vol 65 (2) ◽  
pp. 249-275
Author(s):  
Houssem Eddine Khochemane ◽  
Lamine Bouzettouta ◽  
Salah Zitouni
Keyword(s):  
Elastic System ◽  
Past History ◽  
Nonlinear Damping ◽  
General Decay

New general decay of solutions in a porous-thermoelastic system with infinite memory

2021 ◽  
Vol 500 (1) ◽  
pp. 125136
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Salim A. Messaoudi
Keyword(s):  
General Decay ◽  
Infinite Memory ◽  
Decay Of Solutions

Porous elastic system with nonlinear damping and sources terms

2018 ◽  
Vol 264 (4) ◽  
pp. 2970-3051 ◽  
Author(s):  
Mirelson M. Freitas ◽  
M.L. Santos ◽  
José A. Langa
Keyword(s):  
Elastic System ◽  
Nonlinear Damping

scholarly journals GENERAL DECAY OF SOLUTION FOR A POROUS-ELASTIC SYSTEM WITH WEAK NONLINEAR DISSIPATION

2018 ◽  
Vol 05 (01) ◽  
pp. 9-23
Author(s):  
SEBASTIAO M. S. CORDEIRO ◽  
MAURO L. SANTOS ◽  
CARLOS A. RAPOSO
Keyword(s):  
Elastic System ◽  
General Decay ◽  
Nonlinear Dissipation

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 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.

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