Analysis for the strain gradient theory of porous thermoelasticity

Abstract

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Stabilization for an inhomogeneous porous‐elastic system with temperature and microtemperature

“…[24] considered elastic materials with voids when the heat conduction is of type II, and obtained some decay results. In [15], the authors studied a model involving a strain gradient thermoelastic rod with voids and proved existence and uniqueness, and energy decay property by using semigroup arguments. Alves et al.…”

Time decay of the solution to the Cauchy problem for a three‐dimensional model of nonsimple thermoelasticity

“…2 Therefore, from a mathematical point of view, these materials are characterized by the inclusion of higher order gradients of displacement into a set of independent constitutive variables. 5 These theories account for the effects related to size effects and nanotechnology. 6 This theory has been also applied to elastic solids with small voids or vacuum pores that are in the material.…”

“…6 This theory has been also applied to elastic solids with small voids or vacuum pores that are in the material. 5 Fernández et al 5 analyzed strain gradient thermoelastic one-dimensional rods with voids. Magaña and Quintanilla 3 investigated a one-dimensional model of nonsimple materials with heat conduction of Type III.…”

“…Higher order derivatives are added because they allow to better clarify physical properties of some materials 2 . Therefore, from a mathematical point of view, these materials are characterized by the inclusion of higher order gradients of displacement into a set of independent constitutive variables 5 . These theories account for the effects related to size effects and nanotechnology 6 .…”

“…These theories account for the effects related to size effects and nanotechnology 6 . This theory has been also applied to elastic solids with small voids or vacuum pores that are in the material 5 . Fernández et al 5 analyzed strain gradient thermoelastic one‐dimensional rods with voids.…”