Positive temperatures and a positive kernel in coupled thermoelasticity (Q1073592)

The author considers the coupled and quasi-static theory of linear thermoelasticity for the unidirectional conduction of heat in a homogeneous and isotropic slab whose faces are clamped. In this case the temperature is a solution not of the heat equation but of an integro- partial differential equation. The author studies the decay of an initial distribution of temperature when the faces of the slab are maintained at the reference temperature. It is proved that the distributions of temperature vanishing at the boundary which are positive initially need not remain positive, but distributions which are concave initially do remain positive if the coupling is sufficiently weak. Moreover, when the initial temperature is concave, the temperature variation is bounded above by the solution of the corresponding boundary and initial value problem within uncoupled and quasi-static theory. This is an interesting paper.