ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR POROUS FLEXIBLE STRUCTURES WITH SECOND SOUND THERMAL EFFECT
Abstract
The main idea of this work is to develop a new model that combines
the properties of porous-elastic materials and standard linear solids that
depend in its model on Hooke's law. In addition to the two previous mechanical systems, we have added a thermal eect of second sound which is modeled by a system that link the heat equation with the heat
ow eld equation. The model was introduced on the basis of evolution equations and basic equations for exible-porous materials and a standard solids property whose model is based on Hooke's law. It's about a standard linear model of viscoelasticity for system of exible structure materials with voids coupled to heat waves that propagate at a nite velocity according to Cattaneo's law for thermal conduction. We show a global existence of the weak solutions and we then interest by the decay rate in time of solutions where the exponential stability has been proved. In this study, a systematization, important from a practical point of view, was carried out, devoted to completed studies for thermo-visco-elasticity on fexible structures.
the properties of porous-elastic materials and standard linear solids that
depend in its model on Hooke's law. In addition to the two previous mechanical systems, we have added a thermal eect of second sound which is modeled by a system that link the heat equation with the heat
ow eld equation. The model was introduced on the basis of evolution equations and basic equations for exible-porous materials and a standard solids property whose model is based on Hooke's law. It's about a standard linear model of viscoelasticity for system of exible structure materials with voids coupled to heat waves that propagate at a nite velocity according to Cattaneo's law for thermal conduction. We show a global existence of the weak solutions and we then interest by the decay rate in time of solutions where the exponential stability has been proved. In this study, a systematization, important from a practical point of view, was carried out, devoted to completed studies for thermo-visco-elasticity on fexible structures.
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