Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

@article{Peshkov2017ContinuumMA,
  title={Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations},
  author={Ilya Peshkov and Michal Pavelka and Evgeniy I. Romenski and Miroslav Grmela},
  journal={Continuum Mechanics and Thermodynamics},
  year={2017},
  volume={30},
  pages={1343-1378}
}
Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the… 
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