Phase-lag models for heat conduction and thermoelasticity: Well-posedness and stability results

Cattaneo’s law can be regarded as a formal first order Taylor expansion of a delay equation consisting of Fourier’s law of heat conduction in which a delay parameter (phase lag) is added within the time dependence of the heat flux. Similarly, by including two or three delay parameters, the dual- and three-phase-lag models (developed by Tzou and Choudhuri) allow combinations of Taylor approximations of different orders.

After presenting the phase-lag models, the talk will give an overview of well-posedness and stability results for dual- and three-phase-lag equations of heat conduction and thermoelasticity. We will see that the order of Taylor approximation can decide on well-posedness and that conditions on the phase-lags are needed to guarantee stability. Exemplarily, well-posedness and (in)stability will be shown for a particular three-phase-lag heat equation.