Jump relations and discontinuity waves in conductors with memory

This paper investigates a linear functional of the history of a variable which, along with the derivatives, suffers jump discontinuities. The first purpose is to evaluate the jump of the time and space derivatives, of any order, of the functional. Next, the modelling of conductors with memory is considered, in terms of the history of the temperature gradient, and necessary and sufficient thermodynamic restrictions are established. The propagation and evolution of one-dimensional waves is then investigated. The thermodynamic restrictions are shown to guarantee the finiteness of the wave speed and the decay of the discontinuity.