A new exponential decay result for one-dimensional porous dissipation elasticity from second spectrum viewpoint

2020 ◽  
Vol 101 ◽  
pp. 106061 ◽  
Author(s):  
A.J.A. Ramos ◽  
D.S. Almeida Júnior ◽  
M.M. Freitas ◽  
M.J. Dos Santos
2019 ◽  
Vol 94 ◽  
pp. 30-37 ◽  
Author(s):  
Alain Miranville ◽  
Ramón Quintanilla

2018 ◽  
Vol 24 (9) ◽  
pp. 2713-2725 ◽  
Author(s):  
N. Bazarra ◽  
J.R. Fernández ◽  
M.C. Leseduarte ◽  
A. Magaña ◽  
R. Quintanilla

In this paper we consider the one-dimensional version of thermoelasticity with two porous structures and porous dissipation on one or both of them. We first give an existence and uniqueness result by means of semigroup theory. Exponential decay of the solutions is obtained when porous dissipation is assumed for each porous structure. Later, we consider dissipation only on one of the porous structures and we prove that, under appropriate conditions on the coefficients, there exists undamped solutions. Therefore, asymptotic stability cannot be expected in general. However, we are able to give suitable sufficient conditions for the constitutive coefficients to guarantee the exponential decay of the solutions.


2005 ◽  
Vol 32 (6) ◽  
pp. 652-658 ◽  
Author(s):  
Pablo S. Casas ◽  
Ramón Quintanilla

2019 ◽  
Vol 20 (01) ◽  
pp. 2050002
Author(s):  
C. Cuny ◽  
J. Dedecker ◽  
A. Korepanov ◽  
F. Merlevède

For a large class of quickly mixing dynamical systems, we prove that the error in the almost sure approximation with a Brownian motion is of order [Formula: see text] with [Formula: see text]. Specifically, we consider nonuniformly expanding maps with exponential and stretched exponential decay of correlations, with one-dimensional Hölder continuous observables.


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