Some Results in the Theory of a Cosserat Thermoelastic Body with Microtemperatures and Inner Structure

Marin Marin,Eduard M Craciun,Ioan Tuns,Sorin Vlase,Nicolae Pop

doi:10.3390/sym14030511

Marin Marin, Eduard M Craciun + Show 3 more

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https://doi.org/10.3390/sym14030511

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Abstract

This study is concerned with the theory of Cosserat thermoelastic media, whose micro-particles possess microtemperatures. The mixed initial boundary value problem considered in this context is transformed in a temporally evolutionary equation on a Hilbert space. Using some results from the theory of semigroups, the existence and uniqueness of solution is proved. In the same manner, it approached the continuous dependence of the solution upon initial data and loads. From what we have studied, neither on the internet nor in the databases, we have not found qualitative issues addressed regarding the mixed problem in the context of the theory of thermoelasticity of Cosserat environments, in which the contribution of inner structure and microtemperatures are taken into account.

Highlights

The study of elastic materials with microstructure was initiated by the French Cosserat brothers in a famous book that was published in 1909
In order to complete the mixed problem for the Cosserat thermoelastic bodies with microtemperatures and inner structure, we need to associate the initial data, which we use in the following form: vm(x, 0) = v0m(x), vm(x, 0) = v1m(x), φm(x, 0) = φm0 (x), φm(x, 0) = φm1 (x), φ(x, 0) = φ0(x), φ (x, 0) = φ1(x), (14)
The fact that the reaction of a body to some external actions is influenced by the intimate structure of that body and microtemperatures is ignored [25]

Summary

Introduction

The study of elastic materials with microstructure was initiated by the French Cosserat brothers in a famous book that was published in 1909. To get the main results for the mixed problem in the context of Cosserat thermoelastic bodies with inner structure and microtemperatures, we use a few results from the theory of semi-groups of operators.

Results

Conclusion