Structural stability results for the thermoelasticity of type III (Q2925713)

The paper is concerned with the initial boundary value thermoelasticity problem NEWLINE\[NEWLINE\begin{aligned} &\rho \ddot u_i=\mu \Delta u_i+(\lambda+\mu)u_{j,ji}-\beta\dot\alpha_{,i}\;\text{in}\;\Omega ,\\ &c\ddot \alpha=-\beta \dot u_{i,i}+k\Delta \alpha+b \Delta \dot\alpha\;\text{in}\;\Omega ,\\ &u_i=\tilde{u}_i(\mathbf x),\;\alpha=\tilde\alpha(\mathbf x)\;\text{on}\;\partial\Omega,\\ &\alpha(\mathbf x,0=\alpha^0(\mathbf x),\;{u}_i(\mathbf x,0)={u}_i^0(\mathbf x),\;\dot{u}_i(\mathbf x,0)={\nu}_i^0(\mathbf x),\;\dot\alpha(\mathbf x,0)=\theta^0(\mathbf x). \end{aligned}NEWLINE\]NEWLINE The behavior of a solution \(\{u_i,\alpha\}\) as the specific heat \(c>0\) tends to zero is investigated. The energy method is the main tool used.