On the decay of solutions for porous-elastic systems with history

Pamplona, Paulo Xavier; Rivera, Jaime E. Muñoz; Quintanilla, R.

doi:10.1016/j.jmaa.2011.01.045

Cited by 95 publications

(41 citation statements)

References 24 publications

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“…Pamplona et al [15] proved that when the dissipation mechanisms are of rate type the solutions are analytic. Soufyane [19], Soufyane et al [20,21] and Pamplona et al [16] showed several situations with more than one dissipative mechanism where the exponential decay holds. Let us also mention that Muñoz-Rivera and Quintanilla [13] obtained polynomial rates of decay form for some problems when the decay is not of exponential type.…”

Section: Microthermal Effect Viscoporous Effectmentioning

confidence: 99%

On the time decay of solutions for non-simple elasticity with voids

Liu

Magaña²,

Quintanilla³

2015

Z. Angew. Math. Mech.

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Abstract:In this work we consider the non-simple theory of elastic material with voids and we investigate how the coupling of these two aspects of the material affects the behavior of the solutions. We analyze only two kind of different behavior, slow or exponential decay. We introduce four different dissipation mechanisms in the system and we study, in each case, the effect of this mechanism in the behavior of the solutions.

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Section: Microthermal Effect Viscoporous Effectmentioning

confidence: 99%

On the time decay of solutions for non-simple elasticity with voids

Liu

Magaña²,

Quintanilla³

2015

Z. Angew. Math. Mech.

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“…There is in the literature a huge quantity of publications analyzing this FIGURE 1 A fairy cake and a piece of travertine theory. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] It has been applying to geological materials such as rocks or soils as well as to manufactured materials such as ceramics or pressed powders.…”

Section: Introductionmentioning

confidence: 99%

Exponential decay in one‐dimensional Type II/III thermoelasticity with two porosities

Magaña

Quintanilla

2020

Math Methods in App Sciences

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In this paper, we consider the theory of thermoelasticity with a double porosity structure in the context of the Green-Naghdi Types II and III heat conduction models. For the Type II, the problem is given by four hyperbolic equations, and it is conservative (there is no energy dissipation). We introduce in the system a couple of dissipation mechanisms in order to obtain the exponential decay of the solutions. To be precise, we introduce a pair of the following damping mechanisms: viscoelasticity, viscoporosities, and thermal dissipation. We prove that the system is exponentially stable in three different scenarios: viscoporosity in one structure jointly with thermal dissipation, viscoporosity in each structure, and viscoporosity in one structure jointly with viscoelasticity. However, if viscoelasticity and thermal dissipation are considered together, undamped solutions can be obtained KEYWORDS exponential decay, Type II/III thermoelasticity with double voids, viscosity, viscoporosity MSC CLASSIFICATION74F05; 74F99; 74H40; 35Q74 * 11

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“…The author proved the slow decay of the solutions with respect to the time for elastic-porous materials when there is only one dissipation mechanism in the system: the viscoporosity. After that, a lot of works have been developed to clarify the behavior of the solutions (exponential decay, slow decay, impossibility of localization and/or analyticity) for solids with voids [4,5,11,12,15,16,18,19,20,23,22,24,26,27,28,33], for non-simple materials [10,29] or for mixtures of elastic solids [1,2,3,31,32]. Nevertheless, few attention has been paid up to now to micropolar elastic solids.…”

Section: Introductionmentioning

confidence: 99%

On the time decay of solutions in micropolar viscoelasticity

Leseduarte¹,

Magaña²,

Quintanilla³

2015

Meccanica

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This paper deals with isotropic micropolar viscoelastic materials. It can be said that that kind of materials have two internal structures: the macrostructure, where the elasticity effects are noticed, and the microstructure, where the polarity of the material points allows them to rotate. We introduce, step by step, dissipation mechanisms in both structures, obtain the corresponding system of equations and determine the behavior of its solutions with respect the time.

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On the decay of solutions for porous-elastic systems with history

Cited by 95 publications

References 24 publications

On the time decay of solutions for non-simple elasticity with voids

On the time decay of solutions for non-simple elasticity with voids

Exponential decay in one‐dimensional Type II/III thermoelasticity with two porosities

On the time decay of solutions in micropolar viscoelasticity

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