Nonsimple material problems addressed by the Lagrange’s identity
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
Boundary Value Problems 2013, 2013:135 doi:10.1186/1687-2770-2013-135Published: 20 May 2013
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.