Generalized heat-transport equations: parabolic and hyperbolic models

@article{Rogolino2017GeneralizedHE,
  title={Generalized heat-transport equations: parabolic and hyperbolic models},
  author={Patrizia Rogolino and R{\'o}bert Kov{\'a}cs and P{\'e}ter V{\'a}n and Vito Antonio Cimmelli},
  journal={Continuum Mechanics and Thermodynamics},
  year={2017},
  volume={30},
  pages={1245-1258}
}
We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some… 
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