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Open Access Research

Nonsimple material problems addressed by the Lagrange’s identity

Marin I Marin1*, Ravi P Agarwal2 and SR Mahmoud34

Author Affiliations

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

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

3 Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

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

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Boundary Value Problems 2013, 2013:135  doi:10.1186/1687-2770-2013-135

Published: 20 May 2013

Abstract

Our paper is concerned with some basic theorems for nonsimple thermoelastic materials. By using the Lagrange identity, we prove the uniqueness theorem and some continuous dependence theorems without recourse to any energy conservation law, or to any boundedness assumptions on the thermoelastic coefficients. Moreover, we avoid the use of positive definiteness assumptions on the thermoelastic coefficients.

Keywords:
Lagrange identity; nonsimple materials; uniqueness; continuous dependence