Bounds at the heat absorbed by a deformable body (Q750734)

The author considers a one-dimensional thermoelastic homogeneous body in a heat bath. The temperature is subject to the parabolic \(equation\) k\(\theta\) \({}_{xx}=C\theta_ t+{\dot \xi}(t)\theta\) under the boundary condition \(\theta (0,t)=\theta (L,t)=\tau (t).\) An upper bound for the net heat \(\int^{T}_{0}k(\theta_ x(L,t)- \theta_ t(0,t))dt\) gained by the body is given. The upper bound depends only on \(\tau\) and the initial and final states of the body.