A note on the delayed heat equation: Instability with respect to initial data

By P. Jordan, W. Dai, Ronald E. Mickens. 2008

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On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction (2009, background): “To correct this unrealistic feature, which is known as the ‘paradox of heat conduction’ (PHC), various modifications of Fourier’s law have been proposed over the years, not all of which have been successful (see the illuminating discussion in Jordan et al. (2008)).”
Linear and Quasi-Linear Evolution Equations in Hilbert Spaces (2012, background): “2) with σ > 0 and ε small, include models of heat equations with delay (Li [92], Cattaneo [21], Jordan, Dai and Mickens [67], Liu [104]), where ε is a measure of the delay or heat relaxation time; Maxwell’s equations in ferromagnetic materials (Milani [114]), where ε is a measure of the displacement”