Abstract
In this work, we investigate a one-dimensional porous-elastic system with thermoelasticity of type III. We establish the well-posedness and the stability of the system for the cases of equal and nonequal speeds of wave propagation. At the end, we use some numerical approximations based on finite difference techniques to validate the theoretical results.
Highlights
The study of problems related to elastic solids with voids has attracted the attention of many researchers due to the extensive practical applications of such materials in different fields, such as petroleum industry, foundation engineering, soil mechanics, power technology, biology, material science and so on
They introduced the concept of a continuum theory of granular materials with interstitial voids into the theory of elastic solids with voids
In addition to their usual elastic effects, these materials have a microstructure with the property that the mass at each point is obtained as the product of the mass density of the material matrix by the volume fraction. This latter idea was introduced by Nunziato and Cowin [22] when they developed a nonlinear theory of elastic materials with voids
Summary
The study of problems related to elastic solids with voids has attracted the attention of many researchers due to the extensive practical applications of such materials in different fields, such as petroleum industry, foundation engineering, soil mechanics, power technology, biology, material science and so on. In 1972, Godman and Cowin [12] proposed an extension of the classical elasticity theory to porous media They introduced the concept of a continuum theory of granular materials with interstitial voids into the theory of elastic solids with voids. In addition to their usual elastic effects, these materials have a microstructure with the property that the mass at each point is obtained as the product of the mass density of the material matrix by the volume fraction. He showed that the unique dissipation given by microtemperatures is strong enough to produce exponential stability if and only if: χ μ ρ.
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