Entropy Field Equation

The linear law relating changes in elastic strain and electric and thermal displacement to changes in thermal stress is

$${\partial \over{\partial t}} {\bf \sigma_3} ~=~ \displaystyl... ...\mbox{$\sim$}} ~{\partial \over{\partial t}} {\bf \epsilon_3 }$$ (24)

Using this relationship we find the coupled wave equation for entropy to be  

$${\rm \bf div}~ \lbrace~ \displaystyle \mathop{\mbox{${\bf \k... ...)~\rbrace ~=~ {\partial^2 \over{\partial t^2}} {\bf \epsilon_3}$$ (25)