Discontinuity waves, shock formation and critical temperature in crystals

[摘要] The propagation of discontinuity waves in a rigid heat conductor at low temperatures is studied by using a generalized non-linear Maxwell-Cattaneo equation developed in the framework of extended thermodynamics. The critical time (i.e., the instant in which a shock wave formation occurs) is evaluated in both cases of infinite and finite heat conductivity. The critical temperature <(theta)over tilde >, pointed out in our previous papers concerning the propagation of shock and simple waves, once more plays an important role: in fact, now it determines two different regimes for the wave propagation and this phenomenon, from a mathematical point of view, is related to the loss of the genuine non-linearity when theta = <(theta)over tilde>. In the last sections some numerical results are given and a brief analysis about the evolution of a possible initial wave profile is performed, (C) 1999 Academic Press.

[发布日期] 1999-12-15