Open Access Research

Effect of intrinsic rotations, microstructural expansion and contractions in initial boundary value problem of thermoelastic bodies

Marin I Marin1*, Ravi P Agarwal2 and Ibrahim A Abbas34

Author Affiliations

1 Department of Mathematics, Transilvania University of Brasov, Brasov, Romania

2 Department of Mathematics, Texas A&M University-Kingsville, Kingsville, USA

3 Department of Mathematics, Faculty of Science and Arts-Khulais, King Abdulaziz University, Jeddah, Saudi Arabia

4 Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt

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Boundary Value Problems 2014, 2014:129  doi:10.1186/1687-2770-2014-129

Published: 22 May 2014

Abstract

This study is dedicated to some basic theorems in the thermoelastodynamics of microstretch bodies. Our intention is to show that the presence of the microstretch does not affect the main characteristics of the mixed initial boundary value problem for thermoelastic bodies. The result regarding the uniqueness theorem is derived with no definiteness assumptions on the elastic coefficients and in the absence of the restriction that the conductivity tensor is positive definite. In the last part of the paper we establish a basic relation which leads to the reciprocal theorem and to another uniqueness result.

MSC: 35M30, 35Q74, 74A15, 74A60, 74M25.

Keywords:
thermoelastic; microstretch; seismic waves; earthquake