Initial sensitivity to the boundary in coupled thermoelasticity (Q1081323)

The paper is concerned with a theory of heat conduction in compressible thermoelastic fluids. Let B be a bounded domain whose boundary is impermeable to the fluid. Then it is found that the temperature \(\theta\) in B satisfies \[ \Delta \theta =\frac{\partial \theta}{\partial t}- \frac{(\gamma -1)}{\gamma | B|}\int_{B}\frac{\partial \theta}{\partial t}dv, \] when \(| B|\) is the volume of B, and \(\gamma\) is the ratio \(C_ p/C\) of the specific heat at constant pressure to the specific heat at constant volume. Roughly speaking, a point of B is said to be a point of initial sensitivity to the boundary if the fundamental solution of (*) in B is not asymptotic at the point, as \(t\to 0\), to the fundamental solution obained by replacing B by the whole of Euclidean 3-space. It is shown that as long as \(\gamma >1\), the set of points of initial sensitivity to the boundary contains a domain of positive measure. The author draws conclusions that are in line with his earlier result on the failure of the maximum principle in coupled thermoelasticity [ibid. 86, 1-12 (1984; Zbl 0575.73009)].