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

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 of solutions of a thermoelastic Bresse system with viscoelastic boundary conditions

2021 ◽  
Vol 39 (6) ◽  
pp. 157-182
Author(s):  
Ammar Khemmoudj
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Decay Rates ◽  
General Decay ◽  
Polynomial Decay ◽  
Relaxation Functions ◽  
Bresse System ◽  
Decay Of Solutions ◽  
Special Cases

In this paper we consider a multidimensional thermoviscoelastic system of Bresse type where the heat conduction is given by Green and Naghdi theories. For a wider class of relaxation functions, We show that the dissipation produced by the memory eect is strong enough to produce a general decay results. We establish a general decay results, from which the usual exponential and polynomial decay rates are only special cases.

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